[{"data":1,"prerenderedAt":5844},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fallgemeine-sinusfunktion":546,"formula-related-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fallgemeine-sinusfunktion":5831},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":208,"checks":5691,"conditions":5721,"conditionsHtml":5722,"deprecated":5723,"description":5685,"extension":5724,"figure":5725,"figureCaption":5726,"figureHtml":5788,"formulaId":5789,"latex":5790,"latexHtml":5791,"level":5792,"meta":5793,"navigation":5735,"path":5794,"redirectFrom":5795,"related":5796,"seo":5801,"stem":5802,"subject":583,"summary":5803,"tags":5804,"variables":5810,"__hash__":5830},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fallgemeine-sinusfunktion.md","Allgemeine Sinusfunktion",[550,551,552,553,554,555],"f(x) = a sin(b(x - c)) + d","Sinusfunktion Parameter","Periode berechnen Sinus","Amplitude Sinusfunktion","Sinusfunktion verschieben und strecken","trigonometrische Funktion aufstellen",{"type":557,"value":558,"toc":5684},"minimark",[559,564,676,1544,1796,1800,2054,3095,4010,4258,4731,4735],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572,573,675],"p",{},"Die ",[569,570,571],"strong",{},"allgemeine Sinusfunktion"," entsteht aus ",[574,575,578,621],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,616],"semantics",{},[590,591,592,596,600,603,606,610,613],"mrow",{},[593,594,595],"mi",{},"y",[597,598,599],"mo",{},"=",[593,601,602],{},"sin",[597,604,605],{},"⁡",[597,607,609],{"stretchy":608},"false","(",[593,611,612],{},"x",[597,614,615],{"stretchy":608},")",[617,618,620],"annotation",{"encoding":619},"application\u002Fx-tex","y = \\sin(x)",[574,622,626,653],{"className":623,"ariaHidden":625},[624],"katex-html","true",[574,627,630,635,641,646,650],{"className":628},[629],"base",[574,631],{"className":632,"style":634},[633],"strut","height:0.625em;vertical-align:-0.1944em;",[574,636,595],{"className":637,"style":640},[638,639],"mord","mathnormal","margin-right:0.0359em;",[574,642],{"className":643,"style":645},[644],"mspace","margin-right:0.2778em;",[574,647,599],{"className":648},[649],"mrel",[574,651],{"className":652,"style":645},[644],[574,654,656,660,664,668,671],{"className":655},[629],[574,657],{"className":658,"style":659},[633],"height:1em;vertical-align:-0.25em;",[574,661,602],{"className":662},[663],"mop",[574,665,609],{"className":666},[667],"mopen",[574,669,612],{"className":670},[638,639],[574,672,615],{"className":673},[674],"mclose"," durch Strecken und Verschieben. Jeder Parameter hat eine eigene Wirkung:",[677,678,679,786,1113,1296],"ul",{},[680,681,682,724,725,728,729,785],"li",{},[574,683,685,706],{"className":684},[577],[574,686,688],{"className":687},[581],[583,689,690],{"xmlns":585},[587,691,692,703],{},[590,693,694,698,701],{},[593,695,697],{"mathvariant":696},"normal","∣",[593,699,700],{},"a",[593,702,697],{"mathvariant":696},[617,704,705],{"encoding":619},"|a|",[574,707,709],{"className":708,"ariaHidden":625},[624],[574,710,712,715,718,721],{"className":711},[629],[574,713],{"className":714,"style":659},[633],[574,716,697],{"className":717},[638],[574,719,700],{"className":720},[638,639],[574,722,697],{"className":723},[638]," ist die ",[569,726,727],{},"Amplitude",", der Abstand von der Mittellinie zu Hoch- und Tiefpunkten. Bei ",[574,730,732,753],{"className":731},[577],[574,733,735],{"className":734},[581],[583,736,737],{"xmlns":585},[587,738,739,750],{},[590,740,741,743,746],{},[593,742,700],{},[597,744,745],{},"\u003C",[747,748,749],"mn",{},"0",[617,751,752],{"encoding":619},"a \u003C 0",[574,754,756,775],{"className":755,"ariaHidden":625},[624],[574,757,759,763,766,769,772],{"className":758},[629],[574,760],{"className":761,"style":762},[633],"height:0.5782em;vertical-align:-0.0391em;",[574,764,700],{"className":765},[638,639],[574,767],{"className":768,"style":645},[644],[574,770,745],{"className":771},[649],[574,773],{"className":774,"style":645},[644],[574,776,778,782],{"className":777},[629],[574,779],{"className":780,"style":781},[633],"height:0.6444em;",[574,783,749],{"className":784},[638]," ist der Graph zusätzlich an der Mittellinie gespiegelt.",[680,787,788,818,819,822,823,986,987,1050,1051,1112],{},[574,789,791,805],{"className":790},[577],[574,792,794],{"className":793},[581],[583,795,796],{"xmlns":585},[587,797,798,803],{},[590,799,800],{},[593,801,802],{},"b",[617,804,802],{"encoding":619},[574,806,808],{"className":807,"ariaHidden":625},[624],[574,809,811,815],{"className":810},[629],[574,812],{"className":813,"style":814},[633],"height:0.6944em;",[574,816,802],{"className":817},[638,639]," bestimmt die ",[569,820,821],{},"Periode"," ",[574,824,826,861],{"className":825},[577],[574,827,829],{"className":828},[581],[583,830,831],{"xmlns":585},[587,832,833,858],{},[590,834,835,837,839],{},[593,836,565],{},[597,838,599],{},[840,841,842,850],"mfrac",{},[590,843,844,847],{},[747,845,846],{},"2",[593,848,849],{},"π",[590,851,852,854,856],{},[593,853,697],{"mathvariant":696},[593,855,802],{},[593,857,697],{"mathvariant":696},[617,859,860],{"encoding":619},"p = \\frac{2\\pi}{|b|}",[574,862,864,882],{"className":863,"ariaHidden":625},[624],[574,865,867,870,873,876,879],{"className":866},[629],[574,868],{"className":869,"style":634},[633],[574,871,565],{"className":872},[638,639],[574,874],{"className":875,"style":645},[644],[574,877,599],{"className":878},[649],[574,880],{"className":881,"style":645},[644],[574,883,885,889],{"className":884},[629],[574,886],{"className":887,"style":888},[633],"height:1.3651em;vertical-align:-0.52em;",[574,890,892,896,983],{"className":891},[638],[574,893],{"className":894},[667,895],"nulldelimiter",[574,897,899],{"className":898},[840],[574,900,904,974],{"className":901},[902,903],"vlist-t","vlist-t2",[574,905,908,969],{"className":906},[907],"vlist-r",[574,909,913,940,951],{"className":910,"style":912},[911],"vlist","height:0.8451em;",[574,914,916,921],{"style":915},"top:-2.655em;",[574,917],{"className":918,"style":920},[919],"pstrut","height:3em;",[574,922,928],{"className":923},[924,925,926,927],"sizing","reset-size6","size3","mtight",[574,929,931,934,937],{"className":930},[638,927],[574,932,697],{"className":933},[638,927],[574,935,802],{"className":936},[638,639,927],[574,938,697],{"className":939},[638,927],[574,941,943,946],{"style":942},"top:-3.23em;",[574,944],{"className":945,"style":920},[919],[574,947],{"className":948,"style":950},[949],"frac-line","border-bottom-width:0.04em;",[574,952,954,957],{"style":953},"top:-3.394em;",[574,955],{"className":956,"style":920},[919],[574,958,960],{"className":959},[924,925,926,927],[574,961,963,966],{"className":962},[638,927],[574,964,846],{"className":965},[638,927],[574,967,849],{"className":968,"style":640},[638,639,927],[574,970,973],{"className":971},[972],"vlist-s","​",[574,975,977],{"className":976},[907],[574,978,981],{"className":979,"style":980},[911],"height:0.52em;",[574,982],{},[574,984],{"className":985},[674,895],". Bei ",[574,988,990,1014],{"className":989},[577],[574,991,993],{"className":992},[581],[583,994,995],{"xmlns":585},[587,996,997,1011],{},[590,998,999,1001,1003,1005,1008],{},[593,1000,697],{"mathvariant":696},[593,1002,802],{},[593,1004,697],{"mathvariant":696},[597,1006,1007],{},">",[747,1009,1010],{},"1",[617,1012,1013],{"encoding":619},"|b| > 1",[574,1015,1017,1041],{"className":1016,"ariaHidden":625},[624],[574,1018,1020,1023,1026,1029,1032,1035,1038],{"className":1019},[629],[574,1021],{"className":1022,"style":659},[633],[574,1024,697],{"className":1025},[638],[574,1027,802],{"className":1028},[638,639],[574,1030,697],{"className":1031},[638],[574,1033],{"className":1034,"style":645},[644],[574,1036,1007],{"className":1037},[649],[574,1039],{"className":1040,"style":645},[644],[574,1042,1044,1047],{"className":1043},[629],[574,1045],{"className":1046,"style":781},[633],[574,1048,1010],{"className":1049},[638]," wird der Graph in x-Richtung gestaucht, bei ",[574,1052,1054,1076],{"className":1053},[577],[574,1055,1057],{"className":1056},[581],[583,1058,1059],{"xmlns":585},[587,1060,1061,1073],{},[590,1062,1063,1065,1067,1069,1071],{},[593,1064,697],{"mathvariant":696},[593,1066,802],{},[593,1068,697],{"mathvariant":696},[597,1070,745],{},[747,1072,1010],{},[617,1074,1075],{"encoding":619},"|b| \u003C 1",[574,1077,1079,1103],{"className":1078,"ariaHidden":625},[624],[574,1080,1082,1085,1088,1091,1094,1097,1100],{"className":1081},[629],[574,1083],{"className":1084,"style":659},[633],[574,1086,697],{"className":1087},[638],[574,1089,802],{"className":1090},[638,639],[574,1092,697],{"className":1093},[638],[574,1095],{"className":1096,"style":645},[644],[574,1098,745],{"className":1099},[649],[574,1101],{"className":1102,"style":645},[644],[574,1104,1106,1109],{"className":1105},[629],[574,1107],{"className":1108,"style":781},[633],[574,1110,1010],{"className":1111},[638]," gestreckt.",[680,1114,1115,1145,1146,1174,1175,1226,1227,1295],{},[574,1116,1118,1132],{"className":1117},[577],[574,1119,1121],{"className":1120},[581],[583,1122,1123],{"xmlns":585},[587,1124,1125,1130],{},[590,1126,1127],{},[593,1128,1129],{},"c",[617,1131,1129],{"encoding":619},[574,1133,1135],{"className":1134,"ariaHidden":625},[624],[574,1136,1138,1142],{"className":1137},[629],[574,1139],{"className":1140,"style":1141},[633],"height:0.4306em;",[574,1143,1129],{"className":1144},[638,639]," verschiebt den Graphen um ",[574,1147,1149,1162],{"className":1148},[577],[574,1150,1152],{"className":1151},[581],[583,1153,1154],{"xmlns":585},[587,1155,1156,1160],{},[590,1157,1158],{},[593,1159,1129],{},[617,1161,1129],{"encoding":619},[574,1163,1165],{"className":1164,"ariaHidden":625},[624],[574,1166,1168,1171],{"className":1167},[629],[574,1169],{"className":1170,"style":1141},[633],[574,1172,1129],{"className":1173},[638,639]," nach rechts. Bei ",[574,1176,1178,1196],{"className":1177},[577],[574,1179,1181],{"className":1180},[581],[583,1182,1183],{"xmlns":585},[587,1184,1185,1193],{},[590,1186,1187,1189,1191],{},[593,1188,612],{},[597,1190,599],{},[593,1192,1129],{},[617,1194,1195],{"encoding":619},"x = c",[574,1197,1199,1217],{"className":1198,"ariaHidden":625},[624],[574,1200,1202,1205,1208,1211,1214],{"className":1201},[629],[574,1203],{"className":1204,"style":1141},[633],[574,1206,612],{"className":1207},[638,639],[574,1209],{"className":1210,"style":645},[644],[574,1212,599],{"className":1213},[649],[574,1215],{"className":1216,"style":645},[644],[574,1218,1220,1223],{"className":1219},[629],[574,1221],{"className":1222,"style":1141},[633],[574,1224,1129],{"className":1225},[638,639]," geht er (für ",[574,1228,1230,1253],{"className":1229},[577],[574,1231,1233],{"className":1232},[581],[583,1234,1235],{"xmlns":585},[587,1236,1237,1250],{},[590,1238,1239,1241,1244,1246,1248],{},[593,1240,700],{},[597,1242,1243],{"separator":625},",",[593,1245,802],{},[597,1247,1007],{},[747,1249,749],{},[617,1251,1252],{"encoding":619},"a, b > 0",[574,1254,1256,1286],{"className":1255,"ariaHidden":625},[624],[574,1257,1259,1263,1266,1270,1274,1277,1280,1283],{"className":1258},[629],[574,1260],{"className":1261,"style":1262},[633],"height:0.8889em;vertical-align:-0.1944em;",[574,1264,700],{"className":1265},[638,639],[574,1267,1243],{"className":1268},[1269],"mpunct",[574,1271],{"className":1272,"style":1273},[644],"margin-right:0.1667em;",[574,1275,802],{"className":1276},[638,639],[574,1278],{"className":1279,"style":645},[644],[574,1281,1007],{"className":1282},[649],[574,1284],{"className":1285,"style":645},[644],[574,1287,1289,1292],{"className":1288},[629],[574,1290],{"className":1291,"style":781},[633],[574,1293,749],{"className":1294},[638],") steigend durch die Mittellinie.",[680,1297,1298,1327,1328,1356,1357,1360,1361,1412,1413,1543],{},[574,1299,1301,1315],{"className":1300},[577],[574,1302,1304],{"className":1303},[581],[583,1305,1306],{"xmlns":585},[587,1307,1308,1313],{},[590,1309,1310],{},[593,1311,1312],{},"d",[617,1314,1312],{"encoding":619},[574,1316,1318],{"className":1317,"ariaHidden":625},[624],[574,1319,1321,1324],{"className":1320},[629],[574,1322],{"className":1323,"style":814},[633],[574,1325,1312],{"className":1326},[638,639]," verschiebt ihn um ",[574,1329,1331,1344],{"className":1330},[577],[574,1332,1334],{"className":1333},[581],[583,1335,1336],{"xmlns":585},[587,1337,1338,1342],{},[590,1339,1340],{},[593,1341,1312],{},[617,1343,1312],{"encoding":619},[574,1345,1347],{"className":1346,"ariaHidden":625},[624],[574,1348,1350,1353],{"className":1349},[629],[574,1351],{"className":1352,"style":814},[633],[574,1354,1312],{"className":1355},[638,639]," nach oben. Die ",[569,1358,1359],{},"Mittellinie"," ist ",[574,1362,1364,1382],{"className":1363},[577],[574,1365,1367],{"className":1366},[581],[583,1368,1369],{"xmlns":585},[587,1370,1371,1379],{},[590,1372,1373,1375,1377],{},[593,1374,595],{},[597,1376,599],{},[593,1378,1312],{},[617,1380,1381],{"encoding":619},"y = d",[574,1383,1385,1403],{"className":1384,"ariaHidden":625},[624],[574,1386,1388,1391,1394,1397,1400],{"className":1387},[629],[574,1389],{"className":1390,"style":634},[633],[574,1392,595],{"className":1393,"style":640},[638,639],[574,1395],{"className":1396,"style":645},[644],[574,1398,599],{"className":1399},[649],[574,1401],{"className":1402,"style":645},[644],[574,1404,1406,1409],{"className":1405},[629],[574,1407],{"className":1408,"style":814},[633],[574,1410,1312],{"className":1411},[638,639],", der Wertebereich ",[574,1414,1416,1463],{"className":1415},[577],[574,1417,1419],{"className":1418},[581],[583,1420,1421],{"xmlns":585},[587,1422,1423,1460],{},[590,1424,1425,1428,1430,1433,1435,1437,1439,1442,1446,1448,1451,1453,1455,1457],{},[597,1426,1427],{"stretchy":608},"[",[593,1429,1312],{},[597,1431,1432],{},"−",[593,1434,697],{"mathvariant":696},[593,1436,700],{},[593,1438,697],{"mathvariant":696},[597,1440,1441],{"separator":625},";",[1443,1444,1445],"mtext",{}," ",[593,1447,1312],{},[597,1449,1450],{},"+",[593,1452,697],{"mathvariant":696},[593,1454,700],{},[593,1456,697],{"mathvariant":696},[597,1458,1459],{"stretchy":608},"]",[617,1461,1462],{"encoding":619},"[d - |a|;\\ d + |a|]",[574,1464,1466,1489,1525],{"className":1465,"ariaHidden":625},[624],[574,1467,1469,1472,1475,1478,1482,1486],{"className":1468},[629],[574,1470],{"className":1471,"style":659},[633],[574,1473,1427],{"className":1474},[667],[574,1476,1312],{"className":1477},[638,639],[574,1479],{"className":1480,"style":1481},[644],"margin-right:0.2222em;",[574,1483,1432],{"className":1484},[1485],"mbin",[574,1487],{"className":1488,"style":1481},[644],[574,1490,1492,1495,1498,1501,1504,1507,1510,1513,1516,1519,1522],{"className":1491},[629],[574,1493],{"className":1494,"style":659},[633],[574,1496,697],{"className":1497},[638],[574,1499,700],{"className":1500},[638,639],[574,1502,697],{"className":1503},[638],[574,1505,1441],{"className":1506},[1269],[574,1508,1445],{"className":1509},[644],[574,1511],{"className":1512,"style":1273},[644],[574,1514,1312],{"className":1515},[638,639],[574,1517],{"className":1518,"style":1481},[644],[574,1520,1450],{"className":1521},[1485],[574,1523],{"className":1524,"style":1481},[644],[574,1526,1528,1531,1534,1537,1540],{"className":1527},[629],[574,1529],{"className":1530,"style":659},[633],[574,1532,697],{"className":1533},[638],[574,1535,700],{"className":1536},[638,639],[574,1538,697],{"className":1539},[638],[574,1541,1459],{"className":1542},[674],".",[565,1545,1546,1547,1575,1576,1579,1580,1631,1632,1683,1684,1714,1715,1743,1744,1543],{},"Die Formel setzt voraus, dass ",[574,1548,1550,1563],{"className":1549},[577],[574,1551,1553],{"className":1552},[581],[583,1554,1555],{"xmlns":585},[587,1556,1557,1561],{},[590,1558,1559],{},[593,1560,612],{},[617,1562,612],{"encoding":619},[574,1564,1566],{"className":1565,"ariaHidden":625},[624],[574,1567,1569,1572],{"className":1568},[629],[574,1570],{"className":1571,"style":1141},[633],[574,1573,612],{"className":1574},[638,639]," im ",[569,1577,1578],{},"Bogenmaß"," gemessen wird. Mit ",[574,1581,1583,1601],{"className":1582},[577],[574,1584,1586],{"className":1585},[581],[583,1587,1588],{"xmlns":585},[587,1589,1590,1598],{},[590,1591,1592,1594,1596],{},[593,1593,700],{},[597,1595,599],{},[747,1597,749],{},[617,1599,1600],{"encoding":619},"a = 0",[574,1602,1604,1622],{"className":1603,"ariaHidden":625},[624],[574,1605,1607,1610,1613,1616,1619],{"className":1606},[629],[574,1608],{"className":1609,"style":1141},[633],[574,1611,700],{"className":1612},[638,639],[574,1614],{"className":1615,"style":645},[644],[574,1617,599],{"className":1618},[649],[574,1620],{"className":1621,"style":645},[644],[574,1623,1625,1628],{"className":1624},[629],[574,1626],{"className":1627,"style":781},[633],[574,1629,749],{"className":1630},[638]," oder ",[574,1633,1635,1653],{"className":1634},[577],[574,1636,1638],{"className":1637},[581],[583,1639,1640],{"xmlns":585},[587,1641,1642,1650],{},[590,1643,1644,1646,1648],{},[593,1645,802],{},[597,1647,599],{},[747,1649,749],{},[617,1651,1652],{"encoding":619},"b = 0",[574,1654,1656,1674],{"className":1655,"ariaHidden":625},[624],[574,1657,1659,1662,1665,1668,1671],{"className":1658},[629],[574,1660],{"className":1661,"style":814},[633],[574,1663,802],{"className":1664},[638,639],[574,1666],{"className":1667,"style":645},[644],[574,1669,599],{"className":1670},[649],[574,1672],{"className":1673,"style":645},[644],[574,1675,1677,1680],{"className":1676},[629],[574,1678],{"className":1679,"style":781},[633],[574,1681,749],{"className":1682},[638]," wäre ",[574,1685,1687,1701],{"className":1686},[577],[574,1688,1690],{"className":1689},[581],[583,1691,1692],{"xmlns":585},[587,1693,1694,1699],{},[590,1695,1696],{},[593,1697,1698],{},"f",[617,1700,1698],{"encoding":619},[574,1702,1704],{"className":1703,"ariaHidden":625},[624],[574,1705,1707,1710],{"className":1706},[629],[574,1708],{"className":1709,"style":1262},[633],[574,1711,1698],{"className":1712,"style":1713},[638,639],"margin-right:0.1076em;"," konstant; deshalb sind beide ungleich ",[574,1716,1718,1731],{"className":1717},[577],[574,1719,1721],{"className":1720},[581],[583,1722,1723],{"xmlns":585},[587,1724,1725,1729],{},[590,1726,1727],{},[747,1728,749],{},[617,1730,749],{"encoding":619},[574,1732,1734],{"className":1733,"ariaHidden":625},[624],[574,1735,1737,1740],{"className":1736},[629],[574,1738],{"className":1739,"style":781},[633],[574,1741,749],{"className":1742},[638],". In der Praxis wählt man meist ",[574,1745,1747,1765],{"className":1746},[577],[574,1748,1750],{"className":1749},[581],[583,1751,1752],{"xmlns":585},[587,1753,1754,1762],{},[590,1755,1756,1758,1760],{},[593,1757,802],{},[597,1759,1007],{},[747,1761,749],{},[617,1763,1764],{"encoding":619},"b > 0",[574,1766,1768,1787],{"className":1767,"ariaHidden":625},[624],[574,1769,1771,1775,1778,1781,1784],{"className":1770},[629],[574,1772],{"className":1773,"style":1774},[633],"height:0.7335em;vertical-align:-0.0391em;",[574,1776,802],{"className":1777},[638,639],[574,1779],{"className":1780,"style":645},[644],[574,1782,1007],{"className":1783},[649],[574,1785],{"className":1786,"style":645},[644],[574,1788,1790,1793],{"className":1789},[629],[574,1791],{"className":1792,"style":781},[633],[574,1794,749],{"className":1795},[638],[560,1797,1799],{"id":1798},"beispiele","Beispiele",[565,1801,1802,2053],{},[574,1803,1805,1866],{"className":1804},[577],[574,1806,1808],{"className":1807},[581],[583,1809,1810],{"xmlns":585},[587,1811,1812,1863],{},[590,1813,1814,1816,1818,1820,1822,1824,1827,1830,1832,1834,1837,1839,1841,1843,1845,1855,1857,1859,1861],{},[593,1815,1698],{},[597,1817,609],{"stretchy":608},[593,1819,612],{},[597,1821,615],{"stretchy":608},[597,1823,599],{},[747,1825,1826],{},"3",[597,1828,1829],{},"⋅",[593,1831,602],{},[597,1833,605],{},[597,1835,609],{"fence":625,"stretchy":625,"minsize":1836,"maxsize":1836},"1.2em",[747,1838,846],{},[597,1840,609],{"stretchy":608},[593,1842,612],{},[597,1844,1432],{},[1846,1847,1848],"mstyle",{"scriptlevel":749,"displaystyle":608},[840,1849,1850,1852],{},[593,1851,849],{},[747,1853,1854],{},"4",[597,1856,615],{"stretchy":608},[597,1858,615],{"fence":625,"stretchy":625,"minsize":1836,"maxsize":1836},[597,1860,1450],{},[747,1862,1010],{},[617,1864,1865],{"encoding":619},"f(x) = 3 \\cdot \\sin\\bigl(2(x - \\tfrac{\\pi}{4})\\bigr) + 1",[574,1867,1869,1896,1914,1950,2044],{"className":1868,"ariaHidden":625},[624],[574,1870,1872,1875,1878,1881,1884,1887,1890,1893],{"className":1871},[629],[574,1873],{"className":1874,"style":659},[633],[574,1876,1698],{"className":1877,"style":1713},[638,639],[574,1879,609],{"className":1880},[667],[574,1882,612],{"className":1883},[638,639],[574,1885,615],{"className":1886},[674],[574,1888],{"className":1889,"style":645},[644],[574,1891,599],{"className":1892},[649],[574,1894],{"className":1895,"style":645},[644],[574,1897,1899,1902,1905,1908,1911],{"className":1898},[629],[574,1900],{"className":1901,"style":781},[633],[574,1903,1826],{"className":1904},[638],[574,1906],{"className":1907,"style":1481},[644],[574,1909,1829],{"className":1910},[1485],[574,1912],{"className":1913,"style":1481},[644],[574,1915,1917,1921,1924,1932,1935,1938,1941,1944,1947],{"className":1916},[629],[574,1918],{"className":1919,"style":1920},[633],"height:1.2em;vertical-align:-0.35em;",[574,1922,602],{"className":1923},[663],[574,1925,1927],{"className":1926},[667],[574,1928,609],{"className":1929},[1930,1931],"delimsizing","size1",[574,1933,846],{"className":1934},[638],[574,1936,609],{"className":1937},[667],[574,1939,612],{"className":1940},[638,639],[574,1942],{"className":1943,"style":1481},[644],[574,1945,1432],{"className":1946},[1485],[574,1948],{"className":1949,"style":1481},[644],[574,1951,1953,1956,2026,2029,2035,2038,2041],{"className":1952},[629],[574,1954],{"className":1955,"style":1920},[633],[574,1957,1959,1962,2023],{"className":1958},[638],[574,1960],{"className":1961},[667,895],[574,1963,1965],{"className":1964},[840],[574,1966,1968,2014],{"className":1967},[902,903],[574,1969,1971,2011],{"className":1970},[907],[574,1972,1975,1989,1997],{"className":1973,"style":1974},[911],"height:0.6954em;",[574,1976,1977,1980],{"style":915},[574,1978],{"className":1979,"style":920},[919],[574,1981,1983],{"className":1982},[924,925,926,927],[574,1984,1986],{"className":1985},[638,927],[574,1987,1854],{"className":1988},[638,927],[574,1990,1991,1994],{"style":942},[574,1992],{"className":1993,"style":920},[919],[574,1995],{"className":1996,"style":950},[949],[574,1998,1999,2002],{"style":953},[574,2000],{"className":2001,"style":920},[919],[574,2003,2005],{"className":2004},[924,925,926,927],[574,2006,2008],{"className":2007},[638,927],[574,2009,849],{"className":2010,"style":640},[638,639,927],[574,2012,973],{"className":2013},[972],[574,2015,2017],{"className":2016},[907],[574,2018,2021],{"className":2019,"style":2020},[911],"height:0.345em;",[574,2022],{},[574,2024],{"className":2025},[674,895],[574,2027,615],{"className":2028},[674],[574,2030,2032],{"className":2031},[674],[574,2033,615],{"className":2034},[1930,1931],[574,2036],{"className":2037,"style":1481},[644],[574,2039,1450],{"className":2040},[1485],[574,2042],{"className":2043,"style":1481},[644],[574,2045,2047,2050],{"className":2046},[629],[574,2048],{"className":2049,"style":781},[633],[574,2051,1010],{"className":2052},[638],":",[677,2055,2056,2202,2355],{},[680,2057,2058,2059,2087,2088,2139,2140,1543],{},"Amplitude ",[574,2060,2062,2075],{"className":2061},[577],[574,2063,2065],{"className":2064},[581],[583,2066,2067],{"xmlns":585},[587,2068,2069,2073],{},[590,2070,2071],{},[747,2072,1826],{},[617,2074,1826],{"encoding":619},[574,2076,2078],{"className":2077,"ariaHidden":625},[624],[574,2079,2081,2084],{"className":2080},[629],[574,2082],{"className":2083,"style":781},[633],[574,2085,1826],{"className":2086},[638],", Mittellinie ",[574,2089,2091,2109],{"className":2090},[577],[574,2092,2094],{"className":2093},[581],[583,2095,2096],{"xmlns":585},[587,2097,2098,2106],{},[590,2099,2100,2102,2104],{},[593,2101,595],{},[597,2103,599],{},[747,2105,1010],{},[617,2107,2108],{"encoding":619},"y = 1",[574,2110,2112,2130],{"className":2111,"ariaHidden":625},[624],[574,2113,2115,2118,2121,2124,2127],{"className":2114},[629],[574,2116],{"className":2117,"style":634},[633],[574,2119,595],{"className":2120,"style":640},[638,639],[574,2122],{"className":2123,"style":645},[644],[574,2125,599],{"className":2126},[649],[574,2128],{"className":2129,"style":645},[644],[574,2131,2133,2136],{"className":2132},[629],[574,2134],{"className":2135,"style":781},[633],[574,2137,1010],{"className":2138},[638],", Wertebereich ",[574,2141,2143,2169],{"className":2142},[577],[574,2144,2146],{"className":2145},[581],[583,2147,2148],{"xmlns":585},[587,2149,2150,2166],{},[590,2151,2152,2154,2156,2158,2160,2162,2164],{},[597,2153,1427],{"stretchy":608},[597,2155,1432],{},[747,2157,846],{},[597,2159,1441],{"separator":625},[1443,2161,1445],{},[747,2163,1854],{},[597,2165,1459],{"stretchy":608},[617,2167,2168],{"encoding":619},"[-2;\\ 4]",[574,2170,2172],{"className":2171,"ariaHidden":625},[624],[574,2173,2175,2178,2181,2184,2187,2190,2193,2196,2199],{"className":2174},[629],[574,2176],{"className":2177,"style":659},[633],[574,2179,1427],{"className":2180},[667],[574,2182,1432],{"className":2183},[638],[574,2185,846],{"className":2186},[638],[574,2188,1441],{"className":2189},[1269],[574,2191,1445],{"className":2192},[644],[574,2194],{"className":2195,"style":1273},[644],[574,2197,1854],{"className":2198},[638],[574,2200,1459],{"className":2201},[674],[680,2203,2204,2205,1543],{},"Periode ",[574,2206,2208,2238],{"className":2207},[577],[574,2209,2211],{"className":2210},[581],[583,2212,2213],{"xmlns":585},[587,2214,2215,2235],{},[590,2216,2217,2219,2221,2231,2233],{},[593,2218,565],{},[597,2220,599],{},[840,2222,2223,2229],{},[590,2224,2225,2227],{},[747,2226,846],{},[593,2228,849],{},[747,2230,846],{},[597,2232,599],{},[593,2234,849],{},[617,2236,2237],{"encoding":619},"p = \\frac{2\\pi}{2} = \\pi",[574,2239,2241,2259,2346],{"className":2240,"ariaHidden":625},[624],[574,2242,2244,2247,2250,2253,2256],{"className":2243},[629],[574,2245],{"className":2246,"style":634},[633],[574,2248,565],{"className":2249},[638,639],[574,2251],{"className":2252,"style":645},[644],[574,2254,599],{"className":2255},[649],[574,2257],{"className":2258,"style":645},[644],[574,2260,2262,2266,2337,2340,2343],{"className":2261},[629],[574,2263],{"className":2264,"style":2265},[633],"height:1.1901em;vertical-align:-0.345em;",[574,2267,2269,2272,2334],{"className":2268},[638],[574,2270],{"className":2271},[667,895],[574,2273,2275],{"className":2274},[840],[574,2276,2278,2326],{"className":2277},[902,903],[574,2279,2281,2323],{"className":2280},[907],[574,2282,2284,2298,2306],{"className":2283,"style":912},[911],[574,2285,2286,2289],{"style":915},[574,2287],{"className":2288,"style":920},[919],[574,2290,2292],{"className":2291},[924,925,926,927],[574,2293,2295],{"className":2294},[638,927],[574,2296,846],{"className":2297},[638,927],[574,2299,2300,2303],{"style":942},[574,2301],{"className":2302,"style":920},[919],[574,2304],{"className":2305,"style":950},[949],[574,2307,2308,2311],{"style":953},[574,2309],{"className":2310,"style":920},[919],[574,2312,2314],{"className":2313},[924,925,926,927],[574,2315,2317,2320],{"className":2316},[638,927],[574,2318,846],{"className":2319},[638,927],[574,2321,849],{"className":2322,"style":640},[638,639,927],[574,2324,973],{"className":2325},[972],[574,2327,2329],{"className":2328},[907],[574,2330,2332],{"className":2331,"style":2020},[911],[574,2333],{},[574,2335],{"className":2336},[674,895],[574,2338],{"className":2339,"style":645},[644],[574,2341,599],{"className":2342},[649],[574,2344],{"className":2345,"style":645},[644],[574,2347,2349,2352],{"className":2348},[629],[574,2350],{"className":2351,"style":1141},[633],[574,2353,849],{"className":2354,"style":640},[638,639],[680,2356,2357,2358,2479,2480,986,2798,2849,2850,1543],{},"Der Graph startet bei ",[574,2359,2361,2383],{"className":2360},[577],[574,2362,2364],{"className":2363},[581],[583,2365,2366],{"xmlns":585},[587,2367,2368,2380],{},[590,2369,2370,2372,2374],{},[593,2371,612],{},[597,2373,599],{},[840,2375,2376,2378],{},[593,2377,849],{},[747,2379,1854],{},[617,2381,2382],{"encoding":619},"x = \\frac{\\pi}{4}",[574,2384,2386,2404],{"className":2385,"ariaHidden":625},[624],[574,2387,2389,2392,2395,2398,2401],{"className":2388},[629],[574,2390],{"className":2391,"style":1141},[633],[574,2393,612],{"className":2394},[638,639],[574,2396],{"className":2397,"style":645},[644],[574,2399,599],{"className":2400},[649],[574,2402],{"className":2403,"style":645},[644],[574,2405,2407,2411],{"className":2406},[629],[574,2408],{"className":2409,"style":2410},[633],"height:1.0404em;vertical-align:-0.345em;",[574,2412,2414,2417,2476],{"className":2413},[638],[574,2415],{"className":2416},[667,895],[574,2418,2420],{"className":2419},[840],[574,2421,2423,2468],{"className":2422},[902,903],[574,2424,2426,2465],{"className":2425},[907],[574,2427,2429,2443,2451],{"className":2428,"style":1974},[911],[574,2430,2431,2434],{"style":915},[574,2432],{"className":2433,"style":920},[919],[574,2435,2437],{"className":2436},[924,925,926,927],[574,2438,2440],{"className":2439},[638,927],[574,2441,1854],{"className":2442},[638,927],[574,2444,2445,2448],{"style":942},[574,2446],{"className":2447,"style":920},[919],[574,2449],{"className":2450,"style":950},[949],[574,2452,2453,2456],{"style":953},[574,2454],{"className":2455,"style":920},[919],[574,2457,2459],{"className":2458},[924,925,926,927],[574,2460,2462],{"className":2461},[638,927],[574,2463,849],{"className":2464,"style":640},[638,639,927],[574,2466,973],{"className":2467},[972],[574,2469,2471],{"className":2470},[907],[574,2472,2474],{"className":2473,"style":2020},[911],[574,2475],{},[574,2477],{"className":2478},[674,895]," auf der Mittellinie, ein Viertel der Periode später liegt ein Hochpunkt: ",[574,2481,2483,2539],{"className":2482},[577],[574,2484,2486],{"className":2485},[581],[583,2487,2488],{"xmlns":585},[587,2489,2490,2536],{},[590,2491,2492,2494,2506,2508,2510,2512,2514,2516,2528,2530,2532,2534],{},[593,2493,1698],{},[590,2495,2496,2498,2504],{},[597,2497,609],{"fence":625},[840,2499,2500,2502],{},[593,2501,849],{},[747,2503,846],{},[597,2505,615],{"fence":625},[597,2507,599],{},[747,2509,1826],{},[597,2511,1829],{},[593,2513,602],{},[597,2515,605],{},[590,2517,2518,2520,2526],{},[597,2519,609],{"fence":625},[840,2521,2522,2524],{},[593,2523,849],{},[747,2525,846],{},[597,2527,615],{"fence":625},[597,2529,1450],{},[747,2531,1010],{},[597,2533,599],{},[747,2535,1854],{},[617,2537,2538],{"encoding":619},"f\\left(\\frac{\\pi}{2}\\right) = 3 \\cdot \\sin\\left(\\frac{\\pi}{2}\\right) + 1 = 4",[574,2540,2542,2649,2667,2771,2789],{"className":2541,"ariaHidden":625},[624],[574,2543,2545,2548,2551,2554,2640,2643,2646],{"className":2544},[629],[574,2546],{"className":2547,"style":1920},[633],[574,2549,1698],{"className":2550,"style":1713},[638,639],[574,2552],{"className":2553,"style":1273},[644],[574,2555,2558,2566,2634],{"className":2556},[2557],"minner",[574,2559,2563],{"className":2560,"style":2562},[667,2561],"delimcenter","top:0em;",[574,2564,609],{"className":2565},[1930,1931],[574,2567,2569,2572,2631],{"className":2568},[638],[574,2570],{"className":2571},[667,895],[574,2573,2575],{"className":2574},[840],[574,2576,2578,2623],{"className":2577},[902,903],[574,2579,2581,2620],{"className":2580},[907],[574,2582,2584,2598,2606],{"className":2583,"style":1974},[911],[574,2585,2586,2589],{"style":915},[574,2587],{"className":2588,"style":920},[919],[574,2590,2592],{"className":2591},[924,925,926,927],[574,2593,2595],{"className":2594},[638,927],[574,2596,846],{"className":2597},[638,927],[574,2599,2600,2603],{"style":942},[574,2601],{"className":2602,"style":920},[919],[574,2604],{"className":2605,"style":950},[949],[574,2607,2608,2611],{"style":953},[574,2609],{"className":2610,"style":920},[919],[574,2612,2614],{"className":2613},[924,925,926,927],[574,2615,2617],{"className":2616},[638,927],[574,2618,849],{"className":2619,"style":640},[638,639,927],[574,2621,973],{"className":2622},[972],[574,2624,2626],{"className":2625},[907],[574,2627,2629],{"className":2628,"style":2020},[911],[574,2630],{},[574,2632],{"className":2633},[674,895],[574,2635,2637],{"className":2636,"style":2562},[674,2561],[574,2638,615],{"className":2639},[1930,1931],[574,2641],{"className":2642,"style":645},[644],[574,2644,599],{"className":2645},[649],[574,2647],{"className":2648,"style":645},[644],[574,2650,2652,2655,2658,2661,2664],{"className":2651},[629],[574,2653],{"className":2654,"style":781},[633],[574,2656,1826],{"className":2657},[638],[574,2659],{"className":2660,"style":1481},[644],[574,2662,1829],{"className":2663},[1485],[574,2665],{"className":2666,"style":1481},[644],[574,2668,2670,2673,2676,2679,2762,2765,2768],{"className":2669},[629],[574,2671],{"className":2672,"style":1920},[633],[574,2674,602],{"className":2675},[663],[574,2677],{"className":2678,"style":1273},[644],[574,2680,2682,2688,2756],{"className":2681},[2557],[574,2683,2685],{"className":2684,"style":2562},[667,2561],[574,2686,609],{"className":2687},[1930,1931],[574,2689,2691,2694,2753],{"className":2690},[638],[574,2692],{"className":2693},[667,895],[574,2695,2697],{"className":2696},[840],[574,2698,2700,2745],{"className":2699},[902,903],[574,2701,2703,2742],{"className":2702},[907],[574,2704,2706,2720,2728],{"className":2705,"style":1974},[911],[574,2707,2708,2711],{"style":915},[574,2709],{"className":2710,"style":920},[919],[574,2712,2714],{"className":2713},[924,925,926,927],[574,2715,2717],{"className":2716},[638,927],[574,2718,846],{"className":2719},[638,927],[574,2721,2722,2725],{"style":942},[574,2723],{"className":2724,"style":920},[919],[574,2726],{"className":2727,"style":950},[949],[574,2729,2730,2733],{"style":953},[574,2731],{"className":2732,"style":920},[919],[574,2734,2736],{"className":2735},[924,925,926,927],[574,2737,2739],{"className":2738},[638,927],[574,2740,849],{"className":2741,"style":640},[638,639,927],[574,2743,973],{"className":2744},[972],[574,2746,2748],{"className":2747},[907],[574,2749,2751],{"className":2750,"style":2020},[911],[574,2752],{},[574,2754],{"className":2755},[674,895],[574,2757,2759],{"className":2758,"style":2562},[674,2561],[574,2760,615],{"className":2761},[1930,1931],[574,2763],{"className":2764,"style":1481},[644],[574,2766,1450],{"className":2767},[1485],[574,2769],{"className":2770,"style":1481},[644],[574,2772,2774,2777,2780,2783,2786],{"className":2773},[629],[574,2775],{"className":2776,"style":781},[633],[574,2778,1010],{"className":2779},[638],[574,2781],{"className":2782,"style":645},[644],[574,2784,599],{"className":2785},[649],[574,2787],{"className":2788,"style":645},[644],[574,2790,2792,2795],{"className":2791},[629],[574,2793],{"className":2794,"style":781},[633],[574,2796,1854],{"className":2797},[638],[574,2799,2801,2819],{"className":2800},[577],[574,2802,2804],{"className":2803},[581],[583,2805,2806],{"xmlns":585},[587,2807,2808,2816],{},[590,2809,2810,2812,2814],{},[593,2811,612],{},[597,2813,599],{},[593,2815,849],{},[617,2817,2818],{"encoding":619},"x = \\pi",[574,2820,2822,2840],{"className":2821,"ariaHidden":625},[624],[574,2823,2825,2828,2831,2834,2837],{"className":2824},[629],[574,2826],{"className":2827,"style":1141},[633],[574,2829,612],{"className":2830},[638,639],[574,2832],{"className":2833,"style":645},[644],[574,2835,599],{"className":2836},[649],[574,2838],{"className":2839,"style":645},[644],[574,2841,2843,2846],{"className":2842},[629],[574,2844],{"className":2845,"style":1141},[633],[574,2847,849],{"className":2848,"style":640},[638,639]," liegt ein Tiefpunkt: ",[574,2851,2853,2909],{"className":2852},[577],[574,2854,2856],{"className":2855},[581],[583,2857,2858],{"xmlns":585},[587,2859,2860,2906],{},[590,2861,2862,2864,2866,2868,2870,2872,2874,2876,2878,2880,2896,2898,2900,2902,2904],{},[593,2863,1698],{},[597,2865,609],{"stretchy":608},[593,2867,849],{},[597,2869,615],{"stretchy":608},[597,2871,599],{},[747,2873,1826],{},[597,2875,1829],{},[593,2877,602],{},[597,2879,605],{},[590,2881,2882,2884,2894],{},[597,2883,609],{"fence":625},[840,2885,2886,2892],{},[590,2887,2888,2890],{},[747,2889,1826],{},[593,2891,849],{},[747,2893,846],{},[597,2895,615],{"fence":625},[597,2897,1450],{},[747,2899,1010],{},[597,2901,599],{},[597,2903,1432],{},[747,2905,846],{},[617,2907,2908],{"encoding":619},"f(\\pi) = 3 \\cdot \\sin\\left(\\frac{3\\pi}{2}\\right) + 1 = -2",[574,2910,2912,2939,2957,3064,3082],{"className":2911,"ariaHidden":625},[624],[574,2913,2915,2918,2921,2924,2927,2930,2933,2936],{"className":2914},[629],[574,2916],{"className":2917,"style":659},[633],[574,2919,1698],{"className":2920,"style":1713},[638,639],[574,2922,609],{"className":2923},[667],[574,2925,849],{"className":2926,"style":640},[638,639],[574,2928,615],{"className":2929},[674],[574,2931],{"className":2932,"style":645},[644],[574,2934,599],{"className":2935},[649],[574,2937],{"className":2938,"style":645},[644],[574,2940,2942,2945,2948,2951,2954],{"className":2941},[629],[574,2943],{"className":2944,"style":781},[633],[574,2946,1826],{"className":2947},[638],[574,2949],{"className":2950,"style":1481},[644],[574,2952,1829],{"className":2953},[1485],[574,2955],{"className":2956,"style":1481},[644],[574,2958,2960,2963,2966,2969,3055,3058,3061],{"className":2959},[629],[574,2961],{"className":2962,"style":1920},[633],[574,2964,602],{"className":2965},[663],[574,2967],{"className":2968,"style":1273},[644],[574,2970,2972,2978,3049],{"className":2971},[2557],[574,2973,2975],{"className":2974,"style":2562},[667,2561],[574,2976,609],{"className":2977},[1930,1931],[574,2979,2981,2984,3046],{"className":2980},[638],[574,2982],{"className":2983},[667,895],[574,2985,2987],{"className":2986},[840],[574,2988,2990,3038],{"className":2989},[902,903],[574,2991,2993,3035],{"className":2992},[907],[574,2994,2996,3010,3018],{"className":2995,"style":912},[911],[574,2997,2998,3001],{"style":915},[574,2999],{"className":3000,"style":920},[919],[574,3002,3004],{"className":3003},[924,925,926,927],[574,3005,3007],{"className":3006},[638,927],[574,3008,846],{"className":3009},[638,927],[574,3011,3012,3015],{"style":942},[574,3013],{"className":3014,"style":920},[919],[574,3016],{"className":3017,"style":950},[949],[574,3019,3020,3023],{"style":953},[574,3021],{"className":3022,"style":920},[919],[574,3024,3026],{"className":3025},[924,925,926,927],[574,3027,3029,3032],{"className":3028},[638,927],[574,3030,1826],{"className":3031},[638,927],[574,3033,849],{"className":3034,"style":640},[638,639,927],[574,3036,973],{"className":3037},[972],[574,3039,3041],{"className":3040},[907],[574,3042,3044],{"className":3043,"style":2020},[911],[574,3045],{},[574,3047],{"className":3048},[674,895],[574,3050,3052],{"className":3051,"style":2562},[674,2561],[574,3053,615],{"className":3054},[1930,1931],[574,3056],{"className":3057,"style":1481},[644],[574,3059,1450],{"className":3060},[1485],[574,3062],{"className":3063,"style":1481},[644],[574,3065,3067,3070,3073,3076,3079],{"className":3066},[629],[574,3068],{"className":3069,"style":781},[633],[574,3071,1010],{"className":3072},[638],[574,3074],{"className":3075,"style":645},[644],[574,3077,599],{"className":3078},[649],[574,3080],{"className":3081,"style":645},[644],[574,3083,3085,3089,3092],{"className":3084},[629],[574,3086],{"className":3087,"style":3088},[633],"height:0.7278em;vertical-align:-0.0833em;",[574,3090,1432],{"className":3091},[638],[574,3093,846],{"className":3094},[638],[565,3096,3097,3098,3143,3144,3197,3198,3241,3242,3294,3295,3323,3324,3479,3480,3635,3636,3665,3666,3885,3886,3914,3915,2053],{},"Modellierung: Die Monatsmitteltemperatur einer Stadt schwankt zwischen ",[574,3099,3101,3121],{"className":3100},[577],[574,3102,3104],{"className":3103},[581],[583,3105,3106],{"xmlns":585},[587,3107,3108,3118],{},[590,3109,3110,3112,3115],{},[747,3111,846],{},[1443,3113,3114],{}," ",[1443,3116,3117],{},"°C",[617,3119,3120],{"encoding":619},"2\\,\\text{°C}",[574,3122,3124],{"className":3123,"ariaHidden":625},[624],[574,3125,3127,3130,3133,3136],{"className":3126},[629],[574,3128],{"className":3129,"style":814},[633],[574,3131,846],{"className":3132},[638],[574,3134],{"className":3135,"style":1273},[644],[574,3137,3140],{"className":3138},[638,3139],"text",[574,3141,3117],{"className":3142},[638]," im Januar (",[574,3145,3147,3166],{"className":3146},[577],[574,3148,3150],{"className":3149},[581],[583,3151,3152],{"xmlns":585},[587,3153,3154,3163],{},[590,3155,3156,3159,3161],{},[593,3157,3158],{},"t",[597,3160,599],{},[747,3162,1010],{},[617,3164,3165],{"encoding":619},"t = 1",[574,3167,3169,3188],{"className":3168,"ariaHidden":625},[624],[574,3170,3172,3176,3179,3182,3185],{"className":3171},[629],[574,3173],{"className":3174,"style":3175},[633],"height:0.6151em;",[574,3177,3158],{"className":3178},[638,639],[574,3180],{"className":3181,"style":645},[644],[574,3183,599],{"className":3184},[649],[574,3186],{"className":3187,"style":645},[644],[574,3189,3191,3194],{"className":3190},[629],[574,3192],{"className":3193,"style":781},[633],[574,3195,1010],{"className":3196},[638],") und ",[574,3199,3201,3220],{"className":3200},[577],[574,3202,3204],{"className":3203},[581],[583,3205,3206],{"xmlns":585},[587,3207,3208,3217],{},[590,3209,3210,3213,3215],{},[747,3211,3212],{},"18",[1443,3214,3114],{},[1443,3216,3117],{},[617,3218,3219],{"encoding":619},"18\\,\\text{°C}",[574,3221,3223],{"className":3222,"ariaHidden":625},[624],[574,3224,3226,3229,3232,3235],{"className":3225},[629],[574,3227],{"className":3228,"style":814},[633],[574,3230,3212],{"className":3231},[638],[574,3233],{"className":3234,"style":1273},[644],[574,3236,3238],{"className":3237},[638,3139],[574,3239,3117],{"className":3240},[638]," im Juli (",[574,3243,3245,3264],{"className":3244},[577],[574,3246,3248],{"className":3247},[581],[583,3249,3250],{"xmlns":585},[587,3251,3252,3261],{},[590,3253,3254,3256,3258],{},[593,3255,3158],{},[597,3257,599],{},[747,3259,3260],{},"7",[617,3262,3263],{"encoding":619},"t = 7",[574,3265,3267,3285],{"className":3266,"ariaHidden":625},[624],[574,3268,3270,3273,3276,3279,3282],{"className":3269},[629],[574,3271],{"className":3272,"style":3175},[633],[574,3274,3158],{"className":3275},[638,639],[574,3277],{"className":3278,"style":645},[644],[574,3280,599],{"className":3281},[649],[574,3283],{"className":3284,"style":645},[644],[574,3286,3288,3291],{"className":3287},[629],[574,3289],{"className":3290,"style":781},[633],[574,3292,3260],{"className":3293},[638],"), ",[574,3296,3298,3311],{"className":3297},[577],[574,3299,3301],{"className":3300},[581],[583,3302,3303],{"xmlns":585},[587,3304,3305,3309],{},[590,3306,3307],{},[593,3308,3158],{},[617,3310,3158],{"encoding":619},[574,3312,3314],{"className":3313,"ariaHidden":625},[624],[574,3315,3317,3320],{"className":3316},[629],[574,3318],{"className":3319,"style":3175},[633],[574,3321,3158],{"className":3322},[638,639]," in Monaten. Mittellinie ",[574,3325,3327,3360],{"className":3326},[577],[574,3328,3330],{"className":3329},[581],[583,3331,3332],{"xmlns":585},[587,3333,3334,3357],{},[590,3335,3336,3338,3340,3352,3354],{},[593,3337,1312],{},[597,3339,599],{},[840,3341,3342,3350],{},[590,3343,3344,3346,3348],{},[747,3345,3212],{},[597,3347,1450],{},[747,3349,846],{},[747,3351,846],{},[597,3353,599],{},[747,3355,3356],{},"10",[617,3358,3359],{"encoding":619},"d = \\frac{18 + 2}{2} = 10",[574,3361,3363,3381,3470],{"className":3362,"ariaHidden":625},[624],[574,3364,3366,3369,3372,3375,3378],{"className":3365},[629],[574,3367],{"className":3368,"style":814},[633],[574,3370,1312],{"className":3371},[638,639],[574,3373],{"className":3374,"style":645},[644],[574,3376,599],{"className":3377},[649],[574,3379],{"className":3380,"style":645},[644],[574,3382,3384,3387,3461,3464,3467],{"className":3383},[629],[574,3385],{"className":3386,"style":2265},[633],[574,3388,3390,3393,3458],{"className":3389},[638],[574,3391],{"className":3392},[667,895],[574,3394,3396],{"className":3395},[840],[574,3397,3399,3450],{"className":3398},[902,903],[574,3400,3402,3447],{"className":3401},[907],[574,3403,3405,3419,3427],{"className":3404,"style":912},[911],[574,3406,3407,3410],{"style":915},[574,3408],{"className":3409,"style":920},[919],[574,3411,3413],{"className":3412},[924,925,926,927],[574,3414,3416],{"className":3415},[638,927],[574,3417,846],{"className":3418},[638,927],[574,3420,3421,3424],{"style":942},[574,3422],{"className":3423,"style":920},[919],[574,3425],{"className":3426,"style":950},[949],[574,3428,3429,3432],{"style":953},[574,3430],{"className":3431,"style":920},[919],[574,3433,3435],{"className":3434},[924,925,926,927],[574,3436,3438,3441,3444],{"className":3437},[638,927],[574,3439,3212],{"className":3440},[638,927],[574,3442,1450],{"className":3443},[1485,927],[574,3445,846],{"className":3446},[638,927],[574,3448,973],{"className":3449},[972],[574,3451,3453],{"className":3452},[907],[574,3454,3456],{"className":3455,"style":2020},[911],[574,3457],{},[574,3459],{"className":3460},[674,895],[574,3462],{"className":3463,"style":645},[644],[574,3465,599],{"className":3466},[649],[574,3468],{"className":3469,"style":645},[644],[574,3471,3473,3476],{"className":3472},[629],[574,3474],{"className":3475,"style":781},[633],[574,3477,3356],{"className":3478},[638],", Amplitude ",[574,3481,3483,3516],{"className":3482},[577],[574,3484,3486],{"className":3485},[581],[583,3487,3488],{"xmlns":585},[587,3489,3490,3513],{},[590,3491,3492,3494,3496,3508,3510],{},[593,3493,700],{},[597,3495,599],{},[840,3497,3498,3506],{},[590,3499,3500,3502,3504],{},[747,3501,3212],{},[597,3503,1432],{},[747,3505,846],{},[747,3507,846],{},[597,3509,599],{},[747,3511,3512],{},"8",[617,3514,3515],{"encoding":619},"a = \\frac{18 - 2}{2} = 8",[574,3517,3519,3537,3626],{"className":3518,"ariaHidden":625},[624],[574,3520,3522,3525,3528,3531,3534],{"className":3521},[629],[574,3523],{"className":3524,"style":1141},[633],[574,3526,700],{"className":3527},[638,639],[574,3529],{"className":3530,"style":645},[644],[574,3532,599],{"className":3533},[649],[574,3535],{"className":3536,"style":645},[644],[574,3538,3540,3543,3617,3620,3623],{"className":3539},[629],[574,3541],{"className":3542,"style":2265},[633],[574,3544,3546,3549,3614],{"className":3545},[638],[574,3547],{"className":3548},[667,895],[574,3550,3552],{"className":3551},[840],[574,3553,3555,3606],{"className":3554},[902,903],[574,3556,3558,3603],{"className":3557},[907],[574,3559,3561,3575,3583],{"className":3560,"style":912},[911],[574,3562,3563,3566],{"style":915},[574,3564],{"className":3565,"style":920},[919],[574,3567,3569],{"className":3568},[924,925,926,927],[574,3570,3572],{"className":3571},[638,927],[574,3573,846],{"className":3574},[638,927],[574,3576,3577,3580],{"style":942},[574,3578],{"className":3579,"style":920},[919],[574,3581],{"className":3582,"style":950},[949],[574,3584,3585,3588],{"style":953},[574,3586],{"className":3587,"style":920},[919],[574,3589,3591],{"className":3590},[924,925,926,927],[574,3592,3594,3597,3600],{"className":3593},[638,927],[574,3595,3212],{"className":3596},[638,927],[574,3598,1432],{"className":3599},[1485,927],[574,3601,846],{"className":3602},[638,927],[574,3604,973],{"className":3605},[972],[574,3607,3609],{"className":3608},[907],[574,3610,3612],{"className":3611,"style":2020},[911],[574,3613],{},[574,3615],{"className":3616},[674,895],[574,3618],{"className":3619,"style":645},[644],[574,3621,599],{"className":3622},[649],[574,3624],{"className":3625,"style":645},[644],[574,3627,3629,3632],{"className":3628},[629],[574,3630],{"className":3631,"style":781},[633],[574,3633,3512],{"className":3634},[638],", Periode ",[574,3637,3639,3653],{"className":3638},[577],[574,3640,3642],{"className":3641},[581],[583,3643,3644],{"xmlns":585},[587,3645,3646,3651],{},[590,3647,3648],{},[747,3649,3650],{},"12",[617,3652,3650],{"encoding":619},[574,3654,3656],{"className":3655,"ariaHidden":625},[624],[574,3657,3659,3662],{"className":3658},[629],[574,3660],{"className":3661,"style":781},[633],[574,3663,3650],{"className":3664},[638]," Monate, also ",[574,3667,3669,3704],{"className":3668},[577],[574,3670,3672],{"className":3671},[581],[583,3673,3674],{"xmlns":585},[587,3675,3676,3701],{},[590,3677,3678,3680,3682,3692,3694],{},[593,3679,802],{},[597,3681,599],{},[840,3683,3684,3690],{},[590,3685,3686,3688],{},[747,3687,846],{},[593,3689,849],{},[747,3691,3650],{},[597,3693,599],{},[840,3695,3696,3698],{},[593,3697,849],{},[747,3699,3700],{},"6",[617,3702,3703],{"encoding":619},"b = \\frac{2\\pi}{12} = \\frac{\\pi}{6}",[574,3705,3707,3725,3811],{"className":3706,"ariaHidden":625},[624],[574,3708,3710,3713,3716,3719,3722],{"className":3709},[629],[574,3711],{"className":3712,"style":814},[633],[574,3714,802],{"className":3715},[638,639],[574,3717],{"className":3718,"style":645},[644],[574,3720,599],{"className":3721},[649],[574,3723],{"className":3724,"style":645},[644],[574,3726,3728,3731,3802,3805,3808],{"className":3727},[629],[574,3729],{"className":3730,"style":2265},[633],[574,3732,3734,3737,3799],{"className":3733},[638],[574,3735],{"className":3736},[667,895],[574,3738,3740],{"className":3739},[840],[574,3741,3743,3791],{"className":3742},[902,903],[574,3744,3746,3788],{"className":3745},[907],[574,3747,3749,3763,3771],{"className":3748,"style":912},[911],[574,3750,3751,3754],{"style":915},[574,3752],{"className":3753,"style":920},[919],[574,3755,3757],{"className":3756},[924,925,926,927],[574,3758,3760],{"className":3759},[638,927],[574,3761,3650],{"className":3762},[638,927],[574,3764,3765,3768],{"style":942},[574,3766],{"className":3767,"style":920},[919],[574,3769],{"className":3770,"style":950},[949],[574,3772,3773,3776],{"style":953},[574,3774],{"className":3775,"style":920},[919],[574,3777,3779],{"className":3778},[924,925,926,927],[574,3780,3782,3785],{"className":3781},[638,927],[574,3783,846],{"className":3784},[638,927],[574,3786,849],{"className":3787,"style":640},[638,639,927],[574,3789,973],{"className":3790},[972],[574,3792,3794],{"className":3793},[907],[574,3795,3797],{"className":3796,"style":2020},[911],[574,3798],{},[574,3800],{"className":3801},[674,895],[574,3803],{"className":3804,"style":645},[644],[574,3806,599],{"className":3807},[649],[574,3809],{"className":3810,"style":645},[644],[574,3812,3814,3817],{"className":3813},[629],[574,3815],{"className":3816,"style":2410},[633],[574,3818,3820,3823,3882],{"className":3819},[638],[574,3821],{"className":3822},[667,895],[574,3824,3826],{"className":3825},[840],[574,3827,3829,3874],{"className":3828},[902,903],[574,3830,3832,3871],{"className":3831},[907],[574,3833,3835,3849,3857],{"className":3834,"style":1974},[911],[574,3836,3837,3840],{"style":915},[574,3838],{"className":3839,"style":920},[919],[574,3841,3843],{"className":3842},[924,925,926,927],[574,3844,3846],{"className":3845},[638,927],[574,3847,3700],{"className":3848},[638,927],[574,3850,3851,3854],{"style":942},[574,3852],{"className":3853,"style":920},[919],[574,3855],{"className":3856,"style":950},[949],[574,3858,3859,3862],{"style":953},[574,3860],{"className":3861,"style":920},[919],[574,3863,3865],{"className":3864},[924,925,926,927],[574,3866,3868],{"className":3867},[638,927],[574,3869,849],{"className":3870,"style":640},[638,639,927],[574,3872,973],{"className":3873},[972],[574,3875,3877],{"className":3876},[907],[574,3878,3880],{"className":3879,"style":2020},[911],[574,3881],{},[574,3883],{"className":3884},[674,895],". Der Hochpunkt liegt eine Viertelperiode (",[574,3887,3889,3902],{"className":3888},[577],[574,3890,3892],{"className":3891},[581],[583,3893,3894],{"xmlns":585},[587,3895,3896,3900],{},[590,3897,3898],{},[747,3899,1826],{},[617,3901,1826],{"encoding":619},[574,3903,3905],{"className":3904,"ariaHidden":625},[624],[574,3906,3908,3911],{"className":3907},[629],[574,3909],{"className":3910,"style":781},[633],[574,3912,1826],{"className":3913},[638]," Monate) nach dem Durchgang durch die Mittellinie, also ist ",[574,3916,3918,3944],{"className":3917},[577],[574,3919,3921],{"className":3920},[581],[583,3922,3923],{"xmlns":585},[587,3924,3925,3941],{},[590,3926,3927,3929,3931,3933,3935,3937,3939],{},[593,3928,1129],{},[597,3930,599],{},[747,3932,3260],{},[597,3934,1432],{},[747,3936,1826],{},[597,3938,599],{},[747,3940,1854],{},[617,3942,3943],{"encoding":619},"c = 7 - 3 = 4",[574,3945,3947,3965,3983,4001],{"className":3946,"ariaHidden":625},[624],[574,3948,3950,3953,3956,3959,3962],{"className":3949},[629],[574,3951],{"className":3952,"style":1141},[633],[574,3954,1129],{"className":3955},[638,639],[574,3957],{"className":3958,"style":645},[644],[574,3960,599],{"className":3961},[649],[574,3963],{"className":3964,"style":645},[644],[574,3966,3968,3971,3974,3977,3980],{"className":3967},[629],[574,3969],{"className":3970,"style":3088},[633],[574,3972,3260],{"className":3973},[638],[574,3975],{"className":3976,"style":1481},[644],[574,3978,1432],{"className":3979},[1485],[574,3981],{"className":3982,"style":1481},[644],[574,3984,3986,3989,3992,3995,3998],{"className":3985},[629],[574,3987],{"className":3988,"style":781},[633],[574,3990,1826],{"className":3991},[638],[574,3993],{"className":3994,"style":645},[644],[574,3996,599],{"className":3997},[649],[574,3999],{"className":4000,"style":645},[644],[574,4002,4004,4007],{"className":4003},[629],[574,4005],{"className":4006,"style":781},[633],[574,4008,1854],{"className":4009},[638],[574,4011,4014],{"className":4012},[4013],"katex-display",[574,4015,4017,4075],{"className":4016},[577],[574,4018,4020],{"className":4019},[581],[583,4021,4023],{"xmlns":585,"display":4022},"block",[587,4024,4025,4072],{},[590,4026,4027,4030,4032,4034,4036,4038,4040,4042,4044,4046,4068,4070],{},[593,4028,4029],{},"T",[597,4031,609],{"stretchy":608},[593,4033,3158],{},[597,4035,615],{"stretchy":608},[597,4037,599],{},[747,4039,3512],{},[597,4041,1829],{},[593,4043,602],{},[597,4045,605],{},[590,4047,4048,4050,4056,4058,4060,4062,4064,4066],{},[597,4049,609],{"fence":625},[840,4051,4052,4054],{},[593,4053,849],{},[747,4055,3700],{},[597,4057,609],{"stretchy":608},[593,4059,3158],{},[597,4061,1432],{},[747,4063,1854],{},[597,4065,615],{"stretchy":608},[597,4067,615],{"fence":625},[597,4069,1450],{},[747,4071,3356],{},[617,4073,4074],{"encoding":619},"T(t) = 8 \\cdot \\sin\\left(\\frac{\\pi}{6}(t - 4)\\right) + 10",[574,4076,4078,4106,4124,4249],{"className":4077,"ariaHidden":625},[624],[574,4079,4081,4084,4088,4091,4094,4097,4100,4103],{"className":4080},[629],[574,4082],{"className":4083,"style":659},[633],[574,4085,4029],{"className":4086,"style":4087},[638,639],"margin-right:0.1389em;",[574,4089,609],{"className":4090},[667],[574,4092,3158],{"className":4093},[638,639],[574,4095,615],{"className":4096},[674],[574,4098],{"className":4099,"style":645},[644],[574,4101,599],{"className":4102},[649],[574,4104],{"className":4105,"style":645},[644],[574,4107,4109,4112,4115,4118,4121],{"className":4108},[629],[574,4110],{"className":4111,"style":781},[633],[574,4113,3512],{"className":4114},[638],[574,4116],{"className":4117,"style":1481},[644],[574,4119,1829],{"className":4120},[1485],[574,4122],{"className":4123,"style":1481},[644],[574,4125,4127,4131,4134,4137,4240,4243,4246],{"className":4126},[629],[574,4128],{"className":4129,"style":4130},[633],"height:1.836em;vertical-align:-0.686em;",[574,4132,602],{"className":4133},[663],[574,4135],{"className":4136,"style":1273},[644],[574,4138,4140,4147,4213,4216,4219,4222,4225,4228,4231,4234],{"className":4139},[2557],[574,4141,4143],{"className":4142,"style":2562},[667,2561],[574,4144,609],{"className":4145},[1930,4146],"size2",[574,4148,4150,4153,4210],{"className":4149},[638],[574,4151],{"className":4152},[667,895],[574,4154,4156],{"className":4155},[840],[574,4157,4159,4201],{"className":4158},[902,903],[574,4160,4162,4198],{"className":4161},[907],[574,4163,4166,4178,4186],{"className":4164,"style":4165},[911],"height:1.1076em;",[574,4167,4169,4172],{"style":4168},"top:-2.314em;",[574,4170],{"className":4171,"style":920},[919],[574,4173,4175],{"className":4174},[638],[574,4176,3700],{"className":4177},[638],[574,4179,4180,4183],{"style":942},[574,4181],{"className":4182,"style":920},[919],[574,4184],{"className":4185,"style":950},[949],[574,4187,4189,4192],{"style":4188},"top:-3.677em;",[574,4190],{"className":4191,"style":920},[919],[574,4193,4195],{"className":4194},[638],[574,4196,849],{"className":4197,"style":640},[638,639],[574,4199,973],{"className":4200},[972],[574,4202,4204],{"className":4203},[907],[574,4205,4208],{"className":4206,"style":4207},[911],"height:0.686em;",[574,4209],{},[574,4211],{"className":4212},[674,895],[574,4214,609],{"className":4215},[667],[574,4217,3158],{"className":4218},[638,639],[574,4220],{"className":4221,"style":1481},[644],[574,4223,1432],{"className":4224},[1485],[574,4226],{"className":4227,"style":1481},[644],[574,4229,1854],{"className":4230},[638],[574,4232,615],{"className":4233},[674],[574,4235,4237],{"className":4236,"style":2562},[674,2561],[574,4238,615],{"className":4239},[1930,4146],[574,4241],{"className":4242,"style":1481},[644],[574,4244,1450],{"className":4245},[1485],[574,4247],{"className":4248,"style":1481},[644],[574,4250,4252,4255],{"className":4251},[629],[574,4253],{"className":4254,"style":781},[633],[574,4256,3356],{"className":4257},[638],[565,4259,4260,4261,4493,4494,1543],{},"Probe: ",[574,4262,4264,4314],{"className":4263},[577],[574,4265,4267],{"className":4266},[581],[583,4268,4269],{"xmlns":585},[587,4270,4271,4311],{},[590,4272,4273,4275,4277,4279,4281,4283,4285,4287,4289,4291,4303,4305,4307,4309],{},[593,4274,4029],{},[597,4276,609],{"stretchy":608},[747,4278,3260],{},[597,4280,615],{"stretchy":608},[597,4282,599],{},[747,4284,3512],{},[597,4286,1829],{},[593,4288,602],{},[597,4290,605],{},[590,4292,4293,4295,4301],{},[597,4294,609],{"fence":625},[840,4296,4297,4299],{},[593,4298,849],{},[747,4300,846],{},[597,4302,615],{"fence":625},[597,4304,1450],{},[747,4306,3356],{},[597,4308,599],{},[747,4310,3212],{},[617,4312,4313],{"encoding":619},"T(7) = 8 \\cdot \\sin\\left(\\frac{\\pi}{2}\\right) + 10 = 18",[574,4315,4317,4344,4362,4466,4484],{"className":4316,"ariaHidden":625},[624],[574,4318,4320,4323,4326,4329,4332,4335,4338,4341],{"className":4319},[629],[574,4321],{"className":4322,"style":659},[633],[574,4324,4029],{"className":4325,"style":4087},[638,639],[574,4327,609],{"className":4328},[667],[574,4330,3260],{"className":4331},[638],[574,4333,615],{"className":4334},[674],[574,4336],{"className":4337,"style":645},[644],[574,4339,599],{"className":4340},[649],[574,4342],{"className":4343,"style":645},[644],[574,4345,4347,4350,4353,4356,4359],{"className":4346},[629],[574,4348],{"className":4349,"style":781},[633],[574,4351,3512],{"className":4352},[638],[574,4354],{"className":4355,"style":1481},[644],[574,4357,1829],{"className":4358},[1485],[574,4360],{"className":4361,"style":1481},[644],[574,4363,4365,4368,4371,4374,4457,4460,4463],{"className":4364},[629],[574,4366],{"className":4367,"style":1920},[633],[574,4369,602],{"className":4370},[663],[574,4372],{"className":4373,"style":1273},[644],[574,4375,4377,4383,4451],{"className":4376},[2557],[574,4378,4380],{"className":4379,"style":2562},[667,2561],[574,4381,609],{"className":4382},[1930,1931],[574,4384,4386,4389,4448],{"className":4385},[638],[574,4387],{"className":4388},[667,895],[574,4390,4392],{"className":4391},[840],[574,4393,4395,4440],{"className":4394},[902,903],[574,4396,4398,4437],{"className":4397},[907],[574,4399,4401,4415,4423],{"className":4400,"style":1974},[911],[574,4402,4403,4406],{"style":915},[574,4404],{"className":4405,"style":920},[919],[574,4407,4409],{"className":4408},[924,925,926,927],[574,4410,4412],{"className":4411},[638,927],[574,4413,846],{"className":4414},[638,927],[574,4416,4417,4420],{"style":942},[574,4418],{"className":4419,"style":920},[919],[574,4421],{"className":4422,"style":950},[949],[574,4424,4425,4428],{"style":953},[574,4426],{"className":4427,"style":920},[919],[574,4429,4431],{"className":4430},[924,925,926,927],[574,4432,4434],{"className":4433},[638,927],[574,4435,849],{"className":4436,"style":640},[638,639,927],[574,4438,973],{"className":4439},[972],[574,4441,4443],{"className":4442},[907],[574,4444,4446],{"className":4445,"style":2020},[911],[574,4447],{},[574,4449],{"className":4450},[674,895],[574,4452,4454],{"className":4453,"style":2562},[674,2561],[574,4455,615],{"className":4456},[1930,1931],[574,4458],{"className":4459,"style":1481},[644],[574,4461,1450],{"className":4462},[1485],[574,4464],{"className":4465,"style":1481},[644],[574,4467,4469,4472,4475,4478,4481],{"className":4468},[629],[574,4470],{"className":4471,"style":781},[633],[574,4473,3356],{"className":4474},[638],[574,4476],{"className":4477,"style":645},[644],[574,4479,599],{"className":4480},[649],[574,4482],{"className":4483,"style":645},[644],[574,4485,4487,4490],{"className":4486},[629],[574,4488],{"className":4489,"style":781},[633],[574,4491,3212],{"className":4492},[638]," und ",[574,4495,4497,4549],{"className":4496},[577],[574,4498,4500],{"className":4499},[581],[583,4501,4502],{"xmlns":585},[587,4503,4504,4546],{},[590,4505,4506,4508,4510,4512,4514,4516,4518,4520,4522,4524,4538,4540,4542,4544],{},[593,4507,4029],{},[597,4509,609],{"stretchy":608},[747,4511,1010],{},[597,4513,615],{"stretchy":608},[597,4515,599],{},[747,4517,3512],{},[597,4519,1829],{},[593,4521,602],{},[597,4523,605],{},[590,4525,4526,4528,4530,4536],{},[597,4527,609],{"fence":625},[597,4529,1432],{},[840,4531,4532,4534],{},[593,4533,849],{},[747,4535,846],{},[597,4537,615],{"fence":625},[597,4539,1450],{},[747,4541,3356],{},[597,4543,599],{},[747,4545,846],{},[617,4547,4548],{"encoding":619},"T(1) = 8 \\cdot \\sin\\left(-\\frac{\\pi}{2}\\right) + 10 = 2",[574,4550,4552,4579,4597,4704,4722],{"className":4551,"ariaHidden":625},[624],[574,4553,4555,4558,4561,4564,4567,4570,4573,4576],{"className":4554},[629],[574,4556],{"className":4557,"style":659},[633],[574,4559,4029],{"className":4560,"style":4087},[638,639],[574,4562,609],{"className":4563},[667],[574,4565,1010],{"className":4566},[638],[574,4568,615],{"className":4569},[674],[574,4571],{"className":4572,"style":645},[644],[574,4574,599],{"className":4575},[649],[574,4577],{"className":4578,"style":645},[644],[574,4580,4582,4585,4588,4591,4594],{"className":4581},[629],[574,4583],{"className":4584,"style":781},[633],[574,4586,3512],{"className":4587},[638],[574,4589],{"className":4590,"style":1481},[644],[574,4592,1829],{"className":4593},[1485],[574,4595],{"className":4596,"style":1481},[644],[574,4598,4600,4603,4606,4609,4695,4698,4701],{"className":4599},[629],[574,4601],{"className":4602,"style":1920},[633],[574,4604,602],{"className":4605},[663],[574,4607],{"className":4608,"style":1273},[644],[574,4610,4612,4618,4621,4689],{"className":4611},[2557],[574,4613,4615],{"className":4614,"style":2562},[667,2561],[574,4616,609],{"className":4617},[1930,1931],[574,4619,1432],{"className":4620},[638],[574,4622,4624,4627,4686],{"className":4623},[638],[574,4625],{"className":4626},[667,895],[574,4628,4630],{"className":4629},[840],[574,4631,4633,4678],{"className":4632},[902,903],[574,4634,4636,4675],{"className":4635},[907],[574,4637,4639,4653,4661],{"className":4638,"style":1974},[911],[574,4640,4641,4644],{"style":915},[574,4642],{"className":4643,"style":920},[919],[574,4645,4647],{"className":4646},[924,925,926,927],[574,4648,4650],{"className":4649},[638,927],[574,4651,846],{"className":4652},[638,927],[574,4654,4655,4658],{"style":942},[574,4656],{"className":4657,"style":920},[919],[574,4659],{"className":4660,"style":950},[949],[574,4662,4663,4666],{"style":953},[574,4664],{"className":4665,"style":920},[919],[574,4667,4669],{"className":4668},[924,925,926,927],[574,4670,4672],{"className":4671},[638,927],[574,4673,849],{"className":4674,"style":640},[638,639,927],[574,4676,973],{"className":4677},[972],[574,4679,4681],{"className":4680},[907],[574,4682,4684],{"className":4683,"style":2020},[911],[574,4685],{},[574,4687],{"className":4688},[674,895],[574,4690,4692],{"className":4691,"style":2562},[674,2561],[574,4693,615],{"className":4694},[1930,1931],[574,4696],{"className":4697,"style":1481},[644],[574,4699,1450],{"className":4700},[1485],[574,4702],{"className":4703,"style":1481},[644],[574,4705,4707,4710,4713,4716,4719],{"className":4706},[629],[574,4708],{"className":4709,"style":781},[633],[574,4711,3356],{"className":4712},[638],[574,4714],{"className":4715,"style":645},[644],[574,4717,599],{"className":4718},[649],[574,4720],{"className":4721,"style":645},[644],[574,4723,4725,4728],{"className":4724},[629],[574,4726],{"className":4727,"style":781},[633],[574,4729,846],{"className":4730},[638],[560,4732,4734],{"id":4733},"typische-fehler","Typische Fehler",[677,4736,4737,4944,5491,5652],{},[680,4738,4739,4740,4796,4797,4914,4915,4943],{},"Periode als ",[574,4741,4743,4763],{"className":4742},[577],[574,4744,4746],{"className":4745},[581],[583,4747,4748],{"xmlns":585},[587,4749,4750,4760],{},[590,4751,4752,4754,4756,4758],{},[747,4753,846],{},[593,4755,849],{},[597,4757,1829],{},[593,4759,802],{},[617,4761,4762],{"encoding":619},"2\\pi \\cdot b",[574,4764,4766,4787],{"className":4765,"ariaHidden":625},[624],[574,4767,4769,4772,4775,4778,4781,4784],{"className":4768},[629],[574,4770],{"className":4771,"style":781},[633],[574,4773,846],{"className":4774},[638],[574,4776,849],{"className":4777,"style":640},[638,639],[574,4779],{"className":4780,"style":1481},[644],[574,4782,1829],{"className":4783},[1485],[574,4785],{"className":4786,"style":1481},[644],[574,4788,4790,4793],{"className":4789},[629],[574,4791],{"className":4792,"style":814},[633],[574,4794,802],{"className":4795},[638,639]," berechnen: Richtig ist ",[574,4798,4800,4828],{"className":4799},[577],[574,4801,4803],{"className":4802},[581],[583,4804,4805],{"xmlns":585},[587,4806,4807,4825],{},[590,4808,4809],{},[840,4810,4811,4817],{},[590,4812,4813,4815],{},[747,4814,846],{},[593,4816,849],{},[590,4818,4819,4821,4823],{},[593,4820,697],{"mathvariant":696},[593,4822,802],{},[593,4824,697],{"mathvariant":696},[617,4826,4827],{"encoding":619},"\\frac{2\\pi}{|b|}",[574,4829,4831],{"className":4830,"ariaHidden":625},[624],[574,4832,4834,4837],{"className":4833},[629],[574,4835],{"className":4836,"style":888},[633],[574,4838,4840,4843,4911],{"className":4839},[638],[574,4841],{"className":4842},[667,895],[574,4844,4846],{"className":4845},[840],[574,4847,4849,4903],{"className":4848},[902,903],[574,4850,4852,4900],{"className":4851},[907],[574,4853,4855,4875,4883],{"className":4854,"style":912},[911],[574,4856,4857,4860],{"style":915},[574,4858],{"className":4859,"style":920},[919],[574,4861,4863],{"className":4862},[924,925,926,927],[574,4864,4866,4869,4872],{"className":4865},[638,927],[574,4867,697],{"className":4868},[638,927],[574,4870,802],{"className":4871},[638,639,927],[574,4873,697],{"className":4874},[638,927],[574,4876,4877,4880],{"style":942},[574,4878],{"className":4879,"style":920},[919],[574,4881],{"className":4882,"style":950},[949],[574,4884,4885,4888],{"style":953},[574,4886],{"className":4887,"style":920},[919],[574,4889,4891],{"className":4890},[924,925,926,927],[574,4892,4894,4897],{"className":4893},[638,927],[574,4895,846],{"className":4896},[638,927],[574,4898,849],{"className":4899,"style":640},[638,639,927],[574,4901,973],{"className":4902},[972],[574,4904,4906],{"className":4905},[907],[574,4907,4909],{"className":4908,"style":980},[911],[574,4910],{},[574,4912],{"className":4913},[674,895],". Größeres ",[574,4916,4918,4931],{"className":4917},[577],[574,4919,4921],{"className":4920},[581],[583,4922,4923],{"xmlns":585},[587,4924,4925,4929],{},[590,4926,4927],{},[593,4928,802],{},[617,4930,802],{"encoding":619},[574,4932,4934],{"className":4933,"ariaHidden":625},[624],[574,4935,4937,4940],{"className":4936},[629],[574,4938],{"className":4939,"style":814},[633],[574,4941,802],{"className":4942},[638,639]," bedeutet kürzere Periode.",[680,4945,4946,4947,4975,4976,5293,5294,5392,5393,1543],{},"Die Verschiebung ablesen, ohne ",[574,4948,4950,4963],{"className":4949},[577],[574,4951,4953],{"className":4952},[581],[583,4954,4955],{"xmlns":585},[587,4956,4957,4961],{},[590,4958,4959],{},[593,4960,802],{},[617,4962,802],{"encoding":619},[574,4964,4966],{"className":4965,"ariaHidden":625},[624],[574,4967,4969,4972],{"className":4968},[629],[574,4970],{"className":4971,"style":814},[633],[574,4973,802],{"className":4974},[638,639]," auszuklammern: ",[574,4977,4979,5043],{"className":4978},[577],[574,4980,4982],{"className":4981},[581],[583,4983,4984],{"xmlns":585},[587,4985,4986,5040],{},[590,4987,4988,4990,4992,5010,5012,5014,5016],{},[593,4989,602],{},[597,4991,605],{},[590,4993,4994,4996,4998,5000,5002,5008],{},[597,4995,609],{"fence":625},[747,4997,846],{},[593,4999,612],{},[597,5001,1432],{},[840,5003,5004,5006],{},[593,5005,849],{},[747,5007,846],{},[597,5009,615],{"fence":625},[597,5011,599],{},[593,5013,602],{},[597,5015,605],{},[590,5017,5018,5020,5022,5038],{},[597,5019,609],{"fence":625},[747,5021,846],{},[590,5023,5024,5026,5028,5030,5036],{},[597,5025,609],{"fence":625},[593,5027,612],{},[597,5029,1432],{},[840,5031,5032,5034],{},[593,5033,849],{},[747,5035,1854],{},[597,5037,615],{"fence":625},[597,5039,615],{"fence":625},[617,5041,5042],{"encoding":619},"\\sin\\left(2x - \\frac{\\pi}{2}\\right) = \\sin\\left(2\\left(x - \\frac{\\pi}{4}\\right)\\right)",[574,5044,5046,5165],{"className":5045,"ariaHidden":625},[624],[574,5047,5049,5052,5055,5058,5156,5159,5162],{"className":5048},[629],[574,5050],{"className":5051,"style":1920},[633],[574,5053,602],{"className":5054},[663],[574,5056],{"className":5057,"style":1273},[644],[574,5059,5061,5067,5070,5073,5076,5079,5082,5150],{"className":5060},[2557],[574,5062,5064],{"className":5063,"style":2562},[667,2561],[574,5065,609],{"className":5066},[1930,1931],[574,5068,846],{"className":5069},[638],[574,5071,612],{"className":5072},[638,639],[574,5074],{"className":5075,"style":1481},[644],[574,5077,1432],{"className":5078},[1485],[574,5080],{"className":5081,"style":1481},[644],[574,5083,5085,5088,5147],{"className":5084},[638],[574,5086],{"className":5087},[667,895],[574,5089,5091],{"className":5090},[840],[574,5092,5094,5139],{"className":5093},[902,903],[574,5095,5097,5136],{"className":5096},[907],[574,5098,5100,5114,5122],{"className":5099,"style":1974},[911],[574,5101,5102,5105],{"style":915},[574,5103],{"className":5104,"style":920},[919],[574,5106,5108],{"className":5107},[924,925,926,927],[574,5109,5111],{"className":5110},[638,927],[574,5112,846],{"className":5113},[638,927],[574,5115,5116,5119],{"style":942},[574,5117],{"className":5118,"style":920},[919],[574,5120],{"className":5121,"style":950},[949],[574,5123,5124,5127],{"style":953},[574,5125],{"className":5126,"style":920},[919],[574,5128,5130],{"className":5129},[924,925,926,927],[574,5131,5133],{"className":5132},[638,927],[574,5134,849],{"className":5135,"style":640},[638,639,927],[574,5137,973],{"className":5138},[972],[574,5140,5142],{"className":5141},[907],[574,5143,5145],{"className":5144,"style":2020},[911],[574,5146],{},[574,5148],{"className":5149},[674,895],[574,5151,5153],{"className":5152,"style":2562},[674,2561],[574,5154,615],{"className":5155},[1930,1931],[574,5157],{"className":5158,"style":645},[644],[574,5160,599],{"className":5161},[649],[574,5163],{"className":5164,"style":645},[644],[574,5166,5168,5171,5174,5177],{"className":5167},[629],[574,5169],{"className":5170,"style":1920},[633],[574,5172,602],{"className":5173},[663],[574,5175],{"className":5176,"style":1273},[644],[574,5178,5180,5186,5189,5192,5287],{"className":5179},[2557],[574,5181,5183],{"className":5182,"style":2562},[667,2561],[574,5184,609],{"className":5185},[1930,1931],[574,5187,846],{"className":5188},[638],[574,5190],{"className":5191,"style":1273},[644],[574,5193,5195,5201,5204,5207,5210,5213,5281],{"className":5194},[2557],[574,5196,5198],{"className":5197,"style":2562},[667,2561],[574,5199,609],{"className":5200},[1930,1931],[574,5202,612],{"className":5203},[638,639],[574,5205],{"className":5206,"style":1481},[644],[574,5208,1432],{"className":5209},[1485],[574,5211],{"className":5212,"style":1481},[644],[574,5214,5216,5219,5278],{"className":5215},[638],[574,5217],{"className":5218},[667,895],[574,5220,5222],{"className":5221},[840],[574,5223,5225,5270],{"className":5224},[902,903],[574,5226,5228,5267],{"className":5227},[907],[574,5229,5231,5245,5253],{"className":5230,"style":1974},[911],[574,5232,5233,5236],{"style":915},[574,5234],{"className":5235,"style":920},[919],[574,5237,5239],{"className":5238},[924,925,926,927],[574,5240,5242],{"className":5241},[638,927],[574,5243,1854],{"className":5244},[638,927],[574,5246,5247,5250],{"style":942},[574,5248],{"className":5249,"style":920},[919],[574,5251],{"className":5252,"style":950},[949],[574,5254,5255,5258],{"style":953},[574,5256],{"className":5257,"style":920},[919],[574,5259,5261],{"className":5260},[924,925,926,927],[574,5262,5264],{"className":5263},[638,927],[574,5265,849],{"className":5266,"style":640},[638,639,927],[574,5268,973],{"className":5269},[972],[574,5271,5273],{"className":5272},[907],[574,5274,5276],{"className":5275,"style":2020},[911],[574,5277],{},[574,5279],{"className":5280},[674,895],[574,5282,5284],{"className":5283,"style":2562},[674,2561],[574,5285,615],{"className":5286},[1930,1931],[574,5288,5290],{"className":5289,"style":2562},[674,2561],[574,5291,615],{"className":5292},[1930,1931]," ist um ",[574,5295,5297,5315],{"className":5296},[577],[574,5298,5300],{"className":5299},[581],[583,5301,5302],{"xmlns":585},[587,5303,5304,5312],{},[590,5305,5306],{},[840,5307,5308,5310],{},[593,5309,849],{},[747,5311,1854],{},[617,5313,5314],{"encoding":619},"\\frac{\\pi}{4}",[574,5316,5318],{"className":5317,"ariaHidden":625},[624],[574,5319,5321,5324],{"className":5320},[629],[574,5322],{"className":5323,"style":2410},[633],[574,5325,5327,5330,5389],{"className":5326},[638],[574,5328],{"className":5329},[667,895],[574,5331,5333],{"className":5332},[840],[574,5334,5336,5381],{"className":5335},[902,903],[574,5337,5339,5378],{"className":5338},[907],[574,5340,5342,5356,5364],{"className":5341,"style":1974},[911],[574,5343,5344,5347],{"style":915},[574,5345],{"className":5346,"style":920},[919],[574,5348,5350],{"className":5349},[924,925,926,927],[574,5351,5353],{"className":5352},[638,927],[574,5354,1854],{"className":5355},[638,927],[574,5357,5358,5361],{"style":942},[574,5359],{"className":5360,"style":920},[919],[574,5362],{"className":5363,"style":950},[949],[574,5365,5366,5369],{"style":953},[574,5367],{"className":5368,"style":920},[919],[574,5370,5372],{"className":5371},[924,925,926,927],[574,5373,5375],{"className":5374},[638,927],[574,5376,849],{"className":5377,"style":640},[638,639,927],[574,5379,973],{"className":5380},[972],[574,5382,5384],{"className":5383},[907],[574,5385,5387],{"className":5386,"style":2020},[911],[574,5388],{},[574,5390],{"className":5391},[674,895]," nach rechts verschoben, nicht um ",[574,5394,5396,5414],{"className":5395},[577],[574,5397,5399],{"className":5398},[581],[583,5400,5401],{"xmlns":585},[587,5402,5403,5411],{},[590,5404,5405],{},[840,5406,5407,5409],{},[593,5408,849],{},[747,5410,846],{},[617,5412,5413],{"encoding":619},"\\frac{\\pi}{2}",[574,5415,5417],{"className":5416,"ariaHidden":625},[624],[574,5418,5420,5423],{"className":5419},[629],[574,5421],{"className":5422,"style":2410},[633],[574,5424,5426,5429,5488],{"className":5425},[638],[574,5427],{"className":5428},[667,895],[574,5430,5432],{"className":5431},[840],[574,5433,5435,5480],{"className":5434},[902,903],[574,5436,5438,5477],{"className":5437},[907],[574,5439,5441,5455,5463],{"className":5440,"style":1974},[911],[574,5442,5443,5446],{"style":915},[574,5444],{"className":5445,"style":920},[919],[574,5447,5449],{"className":5448},[924,925,926,927],[574,5450,5452],{"className":5451},[638,927],[574,5453,846],{"className":5454},[638,927],[574,5456,5457,5460],{"style":942},[574,5458],{"className":5459,"style":920},[919],[574,5461],{"className":5462,"style":950},[949],[574,5464,5465,5468],{"style":953},[574,5466],{"className":5467,"style":920},[919],[574,5469,5471],{"className":5470},[924,925,926,927],[574,5472,5474],{"className":5473},[638,927],[574,5475,849],{"className":5476,"style":640},[638,639,927],[574,5478,973],{"className":5479},[972],[574,5481,5483],{"className":5482},[907],[574,5484,5486],{"className":5485,"style":2020},[911],[574,5487],{},[574,5489],{"className":5490},[674,895],[680,5492,5493,5494,5522,5523,1360,5591,5647,5648,5651],{},"Das Vorzeichen von ",[574,5495,5497,5510],{"className":5496},[577],[574,5498,5500],{"className":5499},[581],[583,5501,5502],{"xmlns":585},[587,5503,5504,5508],{},[590,5505,5506],{},[593,5507,1129],{},[617,5509,1129],{"encoding":619},[574,5511,5513],{"className":5512,"ariaHidden":625},[624],[574,5514,5516,5519],{"className":5515},[629],[574,5517],{"className":5518,"style":1141},[633],[574,5520,1129],{"className":5521},[638,639]," umdrehen: Bei ",[574,5524,5526,5552],{"className":5525},[577],[574,5527,5529],{"className":5528},[581],[583,5530,5531],{"xmlns":585},[587,5532,5533,5549],{},[590,5534,5535,5537,5539,5541,5543,5545,5547],{},[593,5536,602],{},[597,5538,605],{},[597,5540,609],{"stretchy":608},[593,5542,612],{},[597,5544,1450],{},[747,5546,1010],{},[597,5548,615],{"stretchy":608},[617,5550,5551],{"encoding":619},"\\sin(x + 1)",[574,5553,5555,5579],{"className":5554,"ariaHidden":625},[624],[574,5556,5558,5561,5564,5567,5570,5573,5576],{"className":5557},[629],[574,5559],{"className":5560,"style":659},[633],[574,5562,602],{"className":5563},[663],[574,5565,609],{"className":5566},[667],[574,5568,612],{"className":5569},[638,639],[574,5571],{"className":5572,"style":1481},[644],[574,5574,1450],{"className":5575},[1485],[574,5577],{"className":5578,"style":1481},[644],[574,5580,5582,5585,5588],{"className":5581},[629],[574,5583],{"className":5584,"style":659},[633],[574,5586,1010],{"className":5587},[638],[574,5589,615],{"className":5590},[674],[574,5592,5594,5614],{"className":5593},[577],[574,5595,5597],{"className":5596},[581],[583,5598,5599],{"xmlns":585},[587,5600,5601,5611],{},[590,5602,5603,5605,5607,5609],{},[593,5604,1129],{},[597,5606,599],{},[597,5608,1432],{},[747,5610,1010],{},[617,5612,5613],{"encoding":619},"c = -1",[574,5615,5617,5635],{"className":5616,"ariaHidden":625},[624],[574,5618,5620,5623,5626,5629,5632],{"className":5619},[629],[574,5621],{"className":5622,"style":1141},[633],[574,5624,1129],{"className":5625},[638,639],[574,5627],{"className":5628,"style":645},[644],[574,5630,599],{"className":5631},[649],[574,5633],{"className":5634,"style":645},[644],[574,5636,5638,5641,5644],{"className":5637},[629],[574,5639],{"className":5640,"style":3088},[633],[574,5642,1432],{"className":5643},[638],[574,5645,1010],{"className":5646},[638],", der Graph ist nach ",[569,5649,5650],{},"links"," verschoben.",[680,5653,5654,5655,5683],{},"Den Taschenrechner im Gradmaß lassen: ",[574,5656,5658,5671],{"className":5657},[577],[574,5659,5661],{"className":5660},[581],[583,5662,5663],{"xmlns":585},[587,5664,5665,5669],{},[590,5666,5667],{},[593,5668,612],{},[617,5670,612],{"encoding":619},[574,5672,5674],{"className":5673,"ariaHidden":625},[624],[574,5675,5677,5680],{"className":5676},[629],[574,5678],{"className":5679,"style":1141},[633],[574,5681,612],{"className":5682},[638,639]," steht im Bogenmaß, der Rechner muss auf RAD stehen.",{"title":5685,"searchDepth":5686,"depth":5686,"links":5687},"",2,[5688,5689,5690],{"id":562,"depth":5686,"text":563},{"id":1798,"depth":5686,"text":1799},{"id":4733,"depth":5686,"text":4734},[5692,5695,5697,5700,5704,5706,5709,5711,5715,5718],{"lhs":5693,"rhs":5694},"a*sin(b*(x + 2*pi\u002Fb - c)) + d","a*sin(b*(x - c)) + d",{"lhs":5696,"rhs":1312},"a*sin(b*(c - c)) + d",{"lhs":5698,"rhs":5699},"a*sin(b*(c + pi\u002F(2*b) - c)) + d","a + d",{"lhs":5701,"rhs":5702,"where":5703},"2*pi\u002Fb","pi",{"b":5686},{"lhs":5705,"rhs":1854},"3*sin(2*(pi\u002F2 - pi\u002F4)) + 1",{"lhs":5707,"rhs":5708},"3*sin(2*(pi - pi\u002F4)) + 1","-2",{"lhs":5710,"rhs":3650},"2*pi\u002F(pi\u002F6)",{"lhs":5712,"rhs":3212,"where":5713},"8*sin(pi\u002F6*(t - 4)) + 10",{"t":5714},7,{"lhs":5712,"rhs":846,"where":5716},{"t":5717},1,{"lhs":5719,"rhs":5720},"sin(2*x - pi\u002F2)","sin(2*(x - pi\u002F4))","a \\neq 0,\\ b \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":5726,"x":5727,"y":5730,"unit":5733,"unitY":5734,"axes":5735,"items":5736},"Graph von f(x) = 3 · sin(2(x − π\u002F4)) + 1 mit Mittellinie y = 1, Amplitude a = 3 und Periode p = π",[5728,5729],-0.4,4.3,[5731,5732],-3.1,4.6,60,34,true,[5737,5742,5747,5754,5759,5762,5765,5768,5774,5776,5780,5784],{"type":5738,"from":5739,"to":5740,"style":5741},"segment",[5728,5717],[5729,5717],"dashed",{"type":5738,"from":5743,"to":5745,"style":5741},[5744,5717],1.5708,[5744,5746],4,{"type":5738,"from":5748,"to":5751,"style":5753},[5749,5750],0.7854,-2.5,[5752,5750],3.927,"muted",{"type":5738,"from":5755,"to":5757,"style":5753},[5749,5756],-2.3,[5749,5758],-2.7,{"type":5738,"from":5760,"to":5761,"style":5753},[5752,5756],[5752,5758],{"type":5763,"expr":5764},"function","3*sin(2*(x - pi\u002F4)) + 1",{"type":5766,"at":5767},"point",[5749,5717],{"type":5769,"at":5770,"text":5773},"label",[5771,5772],1.3,0.59,"(c | d)",{"type":5766,"at":5775},[5744,5746],{"type":5769,"at":5777,"text":700},[5778,5779],1.75,2.5,{"type":5769,"at":5781,"text":565},[5782,5783],2.356,-2.85,{"type":5769,"at":5785,"text":1381},[5786,5787],3.05,1.4,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 282 261.8\" width=\"282\" height=\"261.8\" role=\"img\" aria-label=\"Graph von f(x) = 3 · sin(2(x − π\u002F4)) + 1 mit Mittellinie y = 1, Amplitude a = 3 und Periode p = π\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-general-sine-function-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-general-sine-function-clip\">\u003Crect x=\"0\" y=\"0\" width=\"282\" height=\"261.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"156.4\" x2=\"282\" y2=\"156.4\" class=\"fig-axis\" marker-end=\"url(#fig-general-sine-function-arrow)\"\u002F>\u003Cline x1=\"24\" y1=\"261.8\" x2=\"24\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-general-sine-function-arrow)\"\u002F>\u003Cline x1=\"84\" y1=\"153.4\" x2=\"84\" y2=\"159.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"87\" y=\"170.4\" text-anchor=\"start\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Cline x1=\"144\" y1=\"153.4\" x2=\"144\" y2=\"159.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"147\" y=\"170.4\" text-anchor=\"start\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"204\" y1=\"153.4\" x2=\"204\" y2=\"159.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"207\" y=\"170.4\" text-anchor=\"start\" class=\"fig-tick\">3\u003C\u002Ftext>\u003Cline x1=\"264\" y1=\"153.4\" x2=\"264\" y2=\"159.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"267\" y=\"170.4\" text-anchor=\"start\" class=\"fig-tick\">4\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"258.4\" x2=\"27\" y2=\"258.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"251.39999999999998\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−3\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"224.4\" x2=\"27\" y2=\"224.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"217.4\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−2\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"190.4\" x2=\"27\" y2=\"190.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"183.4\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−1\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"122.4\" x2=\"27\" y2=\"122.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"115.4\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"88.4\" x2=\"27\" y2=\"88.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"81.4\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"54.4\" x2=\"27\" y2=\"54.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"47.4\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">3\u003C\u002Ftext>\u003Cline x1=\"21\" y1=\"20.4\" x2=\"27\" y2=\"20.4\" class=\"fig-axis\"\u002F>\u003Ctext x=\"18\" y=\"13.399999999999999\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">4\u003C\u002Ftext>\u003Ctext x=\"276\" y=\"144.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"36\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cline x1=\"0\" y1=\"122.4\" x2=\"282\" y2=\"122.4\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"118.25\" y1=\"122.4\" x2=\"118.25\" y2=\"20.4\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"71.12\" y1=\"241.4\" x2=\"259.62\" y2=\"241.4\" class=\"fig-muted\"\u002F>\u003Cline x1=\"71.12\" y1=\"234.6\" x2=\"71.12\" y2=\"248.2\" class=\"fig-muted\"\u002F>\u003Cline x1=\"259.62\" y1=\"234.6\" x2=\"259.62\" y2=\"248.2\" class=\"fig-muted\"\u002F>\u003Cpath d=\"M 0 193.46 L 1.18 196.27 L 2.35 198.97 L 3.53 201.55 L 4.7 204.01 L 5.87 206.34 L 7.05 208.55 L 8.23 210.62 L 9.4 212.56 L 10.58 214.36 L 11.75 216.01 L 12.93 217.53 L 14.1 218.9 L 15.28 220.12 L 16.45 221.19 L 17.63 222.11 L 18.8 222.87 L 19.98 223.48 L 21.15 223.94 L 22.33 224.24 L 23.5 224.39 L 24.68 224.37 L 25.85 224.21 L 27.03 223.88 L 28.2 223.4 L 29.38 222.77 L 30.55 221.98 L 31.73 221.04 L 32.9 219.94 L 34.08 218.7 L 35.25 217.31 L 36.43 215.78 L 37.6 214.1 L 38.78 212.28 L 39.95 210.32 L 41.13 208.23 L 42.3 206 L 43.48 203.65 L 44.65 201.18 L 45.83 198.58 L 47 195.86 L 48.18 193.04 L 49.35 190.1 L 50.53 187.06 L 51.7 183.92 L 52.88 180.69 L 54.05 177.37 L 55.23 173.96 L 56.4 170.48 L 57.58 166.92 L 58.75 163.29 L 59.93 159.6 L 61.1 155.85 L 62.28 152.05 L 63.45 148.21 L 64.63 144.32 L 65.8 140.41 L 66.98 136.46 L 68.15 132.49 L 69.33 128.51 L 70.5 124.52 L 71.68 120.53 L 72.85 116.53 L 74.03 112.55 L 75.2 108.58 L 76.38 104.64 L 77.55 100.72 L 78.73 96.83 L 79.9 92.98 L 81.08 89.18 L 82.25 85.43 L 83.43 81.74 L 84.6 78.11 L 85.78 74.54 L 86.95 71.05 L 88.13 67.64 L 89.3 64.31 L 90.48 61.07 L 91.65 57.93 L 92.82 54.88 L 94 51.94 L 95.17 49.11 L 96.35 46.39 L 97.53 43.78 L 98.7 41.3 L 99.88 38.94 L 101.05 36.71 L 102.23 34.61 L 103.4 32.64 L 104.57 30.81 L 105.75 29.12 L 106.92 27.58 L 108.1 26.18 L 109.28 24.93 L 110.45 23.83 L 111.63 22.88 L 112.8 22.08 L 113.98 21.43 L 115.15 20.94 L 116.32 20.61 L 117.5 20.43 L 118.68 20.41 L 119.85 20.55 L 121.03 20.84 L 122.2 21.28 L 123.38 21.89 L 124.55 22.64 L 125.73 23.55 L 126.9 24.61 L 128.08 25.82 L 129.25 27.18 L 130.43 28.69 L 131.6 30.34 L 132.78 32.13 L 133.95 34.06 L 135.13 36.12 L 136.3 38.32 L 137.48 40.64 L 138.65 43.09 L 139.83 45.66 L 141 48.35 L 142.18 51.16 L 143.35 54.07 L 144.53 57.09 L 145.7 60.21 L 146.88 63.42 L 148.05 66.72 L 149.23 70.11 L 150.4 73.58 L 151.58 77.13 L 152.75 80.74 L 153.93 84.42 L 155.1 88.15 L 156.28 91.94 L 157.45 95.78 L 158.63 99.65 L 159.8 103.57 L 160.98 107.5 L 162.15 111.47 L 163.33 115.45 L 164.5 119.44 L 165.68 123.43 L 166.85 127.42 L 168.03 131.41 L 169.2 135.38 L 170.38 139.33 L 171.55 143.26 L 172.73 147.15 L 173.9 151.01 L 175.08 154.82 L 176.25 158.58 L 177.43 162.29 L 178.6 165.93 L 179.78 169.51 L 180.95 173.02 L 182.13 176.45 L 183.3 179.79 L 184.48 183.05 L 185.65 186.21 L 186.83 189.28 L 188 192.25 L 189.18 195.1 L 190.35 197.85 L 191.53 200.48 L 192.7 202.99 L 193.88 205.37 L 195.05 207.63 L 196.23 209.76 L 197.4 211.76 L 198.58 213.61 L 199.75 215.33 L 200.93 216.91 L 202.1 218.34 L 203.28 219.62 L 204.45 220.75 L 205.63 221.74 L 206.8 222.57 L 207.98 223.24 L 209.15 223.77 L 210.33 224.13 L 211.5 224.34 L 212.68 224.4 L 213.85 224.3 L 215.03 224.04 L 216.2 223.62 L 217.38 223.05 L 218.55 222.33 L 219.73 221.45 L 220.9 220.42 L 222.08 219.24 L 223.25 217.92 L 224.43 216.44 L 225.6 214.82 L 226.78 213.06 L 227.95 211.16 L 229.13 209.13 L 230.3 206.96 L 231.48 204.66 L 232.65 202.23 L 233.83 199.69 L 235 197.02 L 236.18 194.24 L 237.35 191.35 L 238.53 188.36 L 239.7 185.26 L 240.88 182.06 L 242.05 178.78 L 243.23 175.41 L 244.4 171.95 L 245.58 168.43 L 246.75 164.83 L 247.93 161.16 L 249.1 157.44 L 250.27 153.66 L 251.45 149.83 L 252.62 145.97 L 253.8 142.06 L 254.98 138.13 L 256.15 134.17 L 257.33 130.19 L 258.5 126.21 L 259.68 122.21 L 260.85 118.22 L 262.03 114.23 L 263.2 110.26 L 264.38 106.3 L 265.55 102.37 L 266.73 98.47 L 267.9 94.6 L 269.08 90.78 L 270.25 87.01 L 271.43 83.29 L 272.6 79.63 L 273.78 76.04 L 274.95 72.52 L 276.13 69.07 L 277.3 65.71 L 278.48 62.43 L 279.65 59.24 L 280.83 56.16 L 282 53.17\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-general-sine-function-clip)\"\u002F>\u003Ccircle cx=\"71.12\" cy=\"122.4\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"102\" y=\"136.34\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">(c | d)\u003C\u002Ftext>\u003Ccircle cx=\"118.25\" cy=\"20.4\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"129\" y=\"71.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"165.36\" y=\"253.3\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">p\u003C\u002Ftext>\u003Ctext x=\"207\" y=\"108.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y = d\u003C\u002Ftext>\u003C\u002Fsvg>","general-sine-function","f(x) = a \\cdot \\sin\\bigl(b(x - c)\\bigr) + d","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) = a \\cdot \\sin\\bigl(b(x - c)\\bigr) + d\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fallgemeine-sinusfunktion",[],[5797,5798,5799,5800],"degrees-radians","sine-right-triangle","vertex-form","exponential-function",{"title":548,"description":5685},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fallgemeine-sinusfunktion","Die allgemeine Sinusfunktion entsteht aus sin(x) durch Strecken und Verschieben; ihre Periode ist 2π\u002F|b|.",[5805,5806,5807,5808,5809],"sinusfunktion","periode","amplitude","verschiebung","trigonometrische funktion",[5811,5814,5817,5820,5823,5826],{"symbol":700,"meaning":5812,"symbolHtml":5813},"Streckfaktor in y-Richtung, |a| ist die Amplitude","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":802,"meaning":5815,"symbolHtml":5816},"Streckfaktor in x-Richtung, bestimmt die Periode 2π\u002F|b|","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1129,"meaning":5818,"symbolHtml":5819},"Verschiebung in x-Richtung (oft Phasenverschiebung genannt)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1312,"meaning":5821,"symbolHtml":5822},"Verschiebung in y-Richtung, die Mittellinie y = d","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":612,"meaning":5824,"symbolHtml":5825},"Eingabewert im Bogenmaß","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5827,"meaning":5828,"symbolHtml":5829},"f(x)","Funktionswert an der Stelle x","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","QtZkJD0N9LUWHbv_7gel5w0xgCan81ksq3L9c2pyBWA",[5832,5835,5838,5841],{"stem":5833,"title":5834,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentialfunktion","Exponentialfunktion",{"stem":5836,"title":5837,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fscheitelpunktform","Scheitelpunktform",{"stem":5839,"title":5840,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck","Sinus im rechtwinkligen Dreieck",{"stem":5842,"title":5843,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fumrechnung-gradmass-bogenmass","Umrechnung Gradmaß in Bogenmaß",1793824273992]