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Nach einer halben Umdrehung wechseln Sinus und Kosinus beide das Vorzeichen, ihr Quotient bleibt gleich.",[565,1032,1033,1034,1065,1066,965,1204,1268,1269,1333],{},"Man kann beliebig viele volle Perioden addieren oder abziehen, deshalb steht in der Formel ",[574,1035,1037,1051],{"className":1036},[577],[574,1038,1040],{"className":1039},[581],[583,1041,1042],{"xmlns":585},[587,1043,1044,1049],{},[590,1045,1046],{},[593,1047,1048],{},"k",[596,1050,1048],{"encoding":598},[574,1052,1054],{"className":1053,"ariaHidden":603},[602],[574,1055,1057,1061],{"className":1056},[607],[574,1058],{"className":1059,"style":1060},[611],"height:0.6944em;",[574,1062,1048],{"className":1063,"style":1064},[616,617],"margin-right:0.0315em;"," für jede ganze Zahl. Der Tangens ist an den Stellen ",[574,1067,1069,1095],{"className":1068},[577],[574,1070,1072],{"className":1071},[581],[583,1073,1074],{"xmlns":585},[587,1075,1076,1092],{},[590,1077,1078,1085,1087,1090],{},[1079,1080,1081,1083],"mfrac",{},[593,1082,827],{},[822,1084,824],{},[664,1086,673],{},[593,1088,1089],{},"m",[593,1091,827],{},[596,1093,1094],{"encoding":598},"\\frac{\\pi}{2} + m\\pi",[574,1096,1098,1194],{"className":1097,"ariaHidden":603},[602],[574,1099,1101,1105,1185,1188,1191],{"className":1100},[607],[574,1102],{"className":1103,"style":1104},[611],"height:1.0404em;vertical-align:-0.345em;",[574,1106,1108,1112,1182],{"className":1107},[616],[574,1109],{"className":1110},[710,1111],"nulldelimiter",[574,1113,1115],{"className":1114},[1079],[574,1116,1119,1173],{"className":1117},[901,1118],"vlist-t2",[574,1120,1122,1168],{"className":1121},[905],[574,1123,1126,1142,1153],{"className":1124,"style":1125},[909],"height:0.6954em;",[574,1127,1129,1133],{"style":1128},"top:-2.655em;",[574,1130],{"className":1131,"style":1132},[916],"height:3em;",[574,1134,1136],{"className":1135},[921,922,923,924],[574,1137,1139],{"className":1138},[616,924],[574,1140,824],{"className":1141},[616,924],[574,1143,1145,1148],{"style":1144},"top:-3.23em;",[574,1146],{"className":1147,"style":1132},[916],[574,1149],{"className":1150,"style":1152},[1151],"frac-line","border-bottom-width:0.04em;",[574,1154,1156,1159],{"style":1155},"top:-3.394em;",[574,1157],{"className":1158,"style":1132},[916],[574,1160,1162],{"className":1161},[921,922,923,924],[574,1163,1165],{"className":1164},[616,924],[574,1166,827],{"className":1167,"style":847},[616,617,924],[574,1169,1172],{"className":1170},[1171],"vlist-s","​",[574,1174,1176],{"className":1175},[905],[574,1177,1180],{"className":1178,"style":1179},[909],"height:0.345em;",[574,1181],{},[574,1183],{"className":1184},[738,1111],[574,1186],{"className":1187,"style":718},[717],[574,1189,673],{"className":1190},[722],[574,1192],{"className":1193,"style":718},[717],[574,1195,1197,1200],{"className":1196},[607],[574,1198],{"className":1199,"style":794},[611],[574,1201,1203],{"className":1202,"style":847},[616,617],"mπ",[574,1205,1207,1226],{"className":1206},[577],[574,1208,1210],{"className":1209},[581],[583,1211,1212],{"xmlns":585},[587,1213,1214,1223],{},[590,1215,1216],{},[862,1217,1218,1221],{},[822,1219,1220],{},"90",[664,1222,869],{},[596,1224,1225],{"encoding":598},"90^\\circ",[574,1227,1229],{"className":1228,"ariaHidden":603},[602],[574,1230,1232,1235,1239],{"className":1231},[607],[574,1233],{"className":1234,"style":882},[611],[574,1236,1238],{"className":1237},[616],"9",[574,1240,1242,1245],{"className":1241},[616],[574,1243,893],{"className":1244},[616],[574,1246,1248],{"className":1247},[897],[574,1249,1251],{"className":1250},[901],[574,1252,1254],{"className":1253},[905],[574,1255,1257],{"className":1256,"style":882},[909],[574,1258,1259,1262],{"style":912},[574,1260],{"className":1261,"style":917},[916],[574,1263,1265],{"className":1264},[921,922,923,924],[574,1266,869],{"className":1267},[722,924],", ",[574,1270,1272,1291],{"className":1271},[577],[574,1273,1275],{"className":1274},[581],[583,1276,1277],{"xmlns":585},[587,1278,1279,1288],{},[590,1280,1281],{},[862,1282,1283,1286],{},[822,1284,1285],{},"270",[664,1287,869],{},[596,1289,1290],{"encoding":598},"270^\\circ",[574,1292,1294],{"className":1293,"ariaHidden":603},[602],[574,1295,1297,1300,1304],{"className":1296},[607],[574,1298],{"className":1299,"style":882},[611],[574,1301,1303],{"className":1302},[616],"27",[574,1305,1307,1310],{"className":1306},[616],[574,1308,893],{"className":1309},[616],[574,1311,1313],{"className":1312},[897],[574,1314,1316],{"className":1315},[901],[574,1317,1319],{"className":1318},[905],[574,1320,1322],{"className":1321,"style":882},[909],[574,1323,1324,1327],{"style":912},[574,1325],{"className":1326,"style":917},[916],[574,1328,1330],{"className":1329},[921,922,923,924],[574,1331,869],{"className":1332},[722,924],", …) nicht definiert.",[565,1335,1336,1337,1396,1397,1458],{},"Damit lässt sich jeder Winkel auf einen Winkel zwischen ",[574,1338,1340,1358],{"className":1339},[577],[574,1341,1343],{"className":1342},[581],[583,1344,1345],{"xmlns":585},[587,1346,1347,1355],{},[590,1348,1349],{},[862,1350,1351,1353],{},[822,1352,893],{},[664,1354,869],{},[596,1356,1357],{"encoding":598},"0^\\circ",[574,1359,1361],{"className":1360,"ariaHidden":603},[602],[574,1362,1364,1367],{"className":1363},[607],[574,1365],{"className":1366,"style":882},[611],[574,1368,1370,1373],{"className":1369},[616],[574,1371,893],{"className":1372},[616],[574,1374,1376],{"className":1375},[897],[574,1377,1379],{"className":1378},[901],[574,1380,1382],{"className":1381},[905],[574,1383,1385],{"className":1384,"style":882},[909],[574,1386,1387,1390],{"style":912},[574,1388],{"className":1389,"style":917},[916],[574,1391,1393],{"className":1392},[921,922,923,924],[574,1394,869],{"className":1395},[722,924]," und ",[574,1398,1400,1417],{"className":1399},[577],[574,1401,1403],{"className":1402},[581],[583,1404,1405],{"xmlns":585},[587,1406,1407,1415],{},[590,1408,1409],{},[862,1410,1411,1413],{},[822,1412,866],{},[664,1414,869],{},[596,1416,872],{"encoding":598},[574,1418,1420],{"className":1419,"ariaHidden":603},[602],[574,1421,1423,1426,1429],{"className":1422},[607],[574,1424],{"className":1425,"style":882},[611],[574,1427,886],{"className":1428},[616],[574,1430,1432,1435],{"className":1431},[616],[574,1433,893],{"className":1434},[616],[574,1436,1438],{"className":1437},[897],[574,1439,1441],{"className":1440},[901],[574,1442,1444],{"className":1443},[905],[574,1445,1447],{"className":1446,"style":882},[909],[574,1448,1449,1452],{"style":912},[574,1450],{"className":1451,"style":917},[916],[574,1453,1455],{"className":1454},[921,922,923,924],[574,1456,869],{"className":1457},[722,924]," zurückführen.",[560,1460,1462],{"id":1461},"beispiele","Beispiele",[574,1464,1467],{"className":1465},[1466],"katex-display",[574,1468,1470,1542],{"className":1469},[577],[574,1471,1473],{"className":1472},[581],[583,1474,1476],{"xmlns":585,"display":1475},"block",[587,1477,1478,1539],{},[590,1479,1480,1483,1486,1493,1495,1497,1499,1501,1508,1510,1516,1518,1520,1522,1524,1530,1532],{},[593,1481,1482],{},"sin",[664,1484,1485],{},"⁡",[862,1487,1488,1491],{},[822,1489,1490],{},"390",[664,1492,869],{},[664,1494,681],{},[593,1496,1482],{},[664,1498,1485],{},[664,1500,667],{"stretchy":666},[862,1502,1503,1506],{},[822,1504,1505],{},"30",[664,1507,869],{},[664,1509,673],{},[862,1511,1512,1514],{},[822,1513,866],{},[664,1515,869],{},[664,1517,678],{"stretchy":666},[664,1519,681],{},[593,1521,1482],{},[664,1523,1485],{},[862,1525,1526,1528],{},[822,1527,1505],{},[664,1529,869],{},[664,1531,681],{},[1079,1533,1534,1537],{},[822,1535,1536],{},"1",[822,1538,824],{},[596,1540,1541],{"encoding":598},"\\sin 390^\\circ = \\sin(30^\\circ + 360^\\circ) = \\sin 30^\\circ = \\frac{1}{2}",[574,1543,1545,1603,1657,1707,1760],{"className":1544,"ariaHidden":603},[602],[574,1546,1548,1552,1556,1560,1564,1594,1597,1600],{"className":1547},[607],[574,1549],{"className":1550,"style":1551},[611],"height:0.7241em;",[574,1553,1482],{"className":1554},[1555],"mop",[574,1557],{"className":1558,"style":1559},[717],"margin-right:0.1667em;",[574,1561,1563],{"className":1562},[616],"39",[574,1565,1567,1570],{"className":1566},[616],[574,1568,893],{"className":1569},[616],[574,1571,1573],{"className":1572},[897],[574,1574,1576],{"className":1575},[901],[574,1577,1579],{"className":1578},[905],[574,1580,1582],{"className":1581,"style":1551},[909],[574,1583,1585,1588],{"style":1584},"top:-3.113em;margin-right:0.05em;",[574,1586],{"className":1587,"style":917},[916],[574,1589,1591],{"className":1590},[921,922,923,924],[574,1592,869],{"className":1593},[722,924],[574,1595],{"className":1596,"style":742},[717],[574,1598,681],{"className":1599},[746],[574,1601],{"className":1602,"style":742},[717],[574,1604,1606,1609,1612,1615,1619,1648,1651,1654],{"className":1605},[607],[574,1607],{"className":1608,"style":702},[611],[574,1610,1482],{"className":1611},[1555],[574,1613,667],{"className":1614},[710],[574,1616,1618],{"className":1617},[616],"3",[574,1620,1622,1625],{"className":1621},[616],[574,1623,893],{"className":1624},[616],[574,1626,1628],{"className":1627},[897],[574,1629,1631],{"className":1630},[901],[574,1632,1634],{"className":1633},[905],[574,1635,1637],{"className":1636,"style":1551},[909],[574,1638,1639,1642],{"style":1584},[574,1640],{"className":1641,"style":917},[916],[574,1643,1645],{"className":1644},[921,922,923,924],[574,1646,869],{"className":1647},[722,924],[574,1649],{"className":1650,"style":718},[717],[574,1652,673],{"className":1653},[722],[574,1655],{"className":1656,"style":718},[717],[574,1658,1660,1663,1666,1695,1698,1701,1704],{"className":1659},[607],[574,1661],{"className":1662,"style":702},[611],[574,1664,886],{"className":1665},[616],[574,1667,1669,1672],{"className":1668},[616],[574,1670,893],{"className":1671},[616],[574,1673,1675],{"className":1674},[897],[574,1676,1678],{"className":1677},[901],[574,1679,1681],{"className":1680},[905],[574,1682,1684],{"className":1683,"style":1551},[909],[574,1685,1686,1689],{"style":1584},[574,1687],{"className":1688,"style":917},[916],[574,1690,1692],{"className":1691},[921,922,923,924],[574,1693,869],{"className":1694},[722,924],[574,1696,678],{"className":1697},[738],[574,1699],{"className":1700,"style":742},[717],[574,1702,681],{"className":1703},[746],[574,1705],{"className":1706,"style":742},[717],[574,1708,1710,1713,1716,1719,1722,1751,1754,1757],{"className":1709},[607],[574,1711],{"className":1712,"style":1551},[611],[574,1714,1482],{"className":1715},[1555],[574,1717],{"className":1718,"style":1559},[717],[574,1720,1618],{"className":1721},[616],[574,1723,1725,1728],{"className":1724},[616],[574,1726,893],{"className":1727},[616],[574,1729,1731],{"className":1730},[897],[574,1732,1734],{"className":1733},[901],[574,1735,1737],{"className":1736},[905],[574,1738,1740],{"className":1739,"style":1551},[909],[574,1741,1742,1745],{"style":1584},[574,1743],{"className":1744,"style":917},[916],[574,1746,1748],{"className":1747},[921,922,923,924],[574,1749,869],{"className":1750},[722,924],[574,1752],{"className":1753,"style":742},[717],[574,1755,681],{"className":1756},[746],[574,1758],{"className":1759,"style":742},[717],[574,1761,1763,1767],{"className":1762},[607],[574,1764],{"className":1765,"style":1766},[611],"height:2.0074em;vertical-align:-0.686em;",[574,1768,1770,1773,1830],{"className":1769},[616],[574,1771],{"className":1772},[710,1111],[574,1774,1776],{"className":1775},[1079],[574,1777,1779,1821],{"className":1778},[901,1118],[574,1780,1782,1818],{"className":1781},[905],[574,1783,1786,1798,1806],{"className":1784,"style":1785},[909],"height:1.3214em;",[574,1787,1789,1792],{"style":1788},"top:-2.314em;",[574,1790],{"className":1791,"style":1132},[916],[574,1793,1795],{"className":1794},[616],[574,1796,824],{"className":1797},[616],[574,1799,1800,1803],{"style":1144},[574,1801],{"className":1802,"style":1132},[916],[574,1804],{"className":1805,"style":1152},[1151],[574,1807,1809,1812],{"style":1808},"top:-3.677em;",[574,1810],{"className":1811,"style":1132},[916],[574,1813,1815],{"className":1814},[616],[574,1816,1536],{"className":1817},[616],[574,1819,1172],{"className":1820},[1171],[574,1822,1824],{"className":1823},[905],[574,1825,1828],{"className":1826,"style":1827},[909],"height:0.686em;",[574,1829],{},[574,1831],{"className":1832},[738,1111],[574,1834,1836],{"className":1835},[1466],[574,1837,1839,1915],{"className":1838},[577],[574,1840,1842],{"className":1841},[581],[583,1843,1844],{"xmlns":585,"display":1475},[587,1845,1846,1912],{},[590,1847,1848,1851,1853,1855,1858,1865,1867,1869,1871,1873,1875,1882,1884,1890,1892,1894,1896,1898,1904,1906],{},[593,1849,1850],{},"cos",[664,1852,1485],{},[664,1854,667],{"stretchy":666},[664,1856,1857],{},"−",[862,1859,1860,1863],{},[822,1861,1862],{},"300",[664,1864,869],{},[664,1866,678],{"stretchy":666},[664,1868,681],{},[593,1870,1850],{},[664,1872,1485],{},[664,1874,667],{"stretchy":666},[862,1876,1877,1880],{},[822,1878,1879],{},"60",[664,1881,869],{},[664,1883,1857],{},[862,1885,1886,1888],{},[822,1887,866],{},[664,1889,869],{},[664,1891,678],{"stretchy":666},[664,1893,681],{},[593,1895,1850],{},[664,1897,1485],{},[862,1899,1900,1902],{},[822,1901,1879],{},[664,1903,869],{},[664,1905,681],{},[1079,1907,1908,1910],{},[822,1909,1536],{},[822,1911,824],{},[596,1913,1914],{"encoding":598},"\\cos(-300^\\circ) = \\cos(60^\\circ - 360^\\circ) = \\cos 60^\\circ = \\frac{1}{2}",[574,1916,1918,1977,2031,2081,2134],{"className":1917,"ariaHidden":603},[602],[574,1919,1921,1924,1927,1930,1933,1936,1965,1968,1971,1974],{"className":1920},[607],[574,1922],{"className":1923,"style":702},[611],[574,1925,1850],{"className":1926},[1555],[574,1928,667],{"className":1929},[710],[574,1931,1857],{"className":1932},[616],[574,1934,1505],{"className":1935},[616],[574,1937,1939,1942],{"className":1938},[616],[574,1940,893],{"className":1941},[616],[574,1943,1945],{"className":1944},[897],[574,1946,1948],{"className":1947},[901],[574,1949,1951],{"className":1950},[905],[574,1952,1954],{"className":1953,"style":1551},[909],[574,1955,1956,1959],{"style":1584},[574,1957],{"className":1958,"style":917},[916],[574,1960,1962],{"className":1961},[921,922,923,924],[574,1963,869],{"className":1964},[722,924],[574,1966,678],{"className":1967},[738],[574,1969],{"className":1970,"style":742},[717],[574,1972,681],{"className":1973},[746],[574,1975],{"className":1976,"style":742},[717],[574,1978,1980,1983,1986,1989,1993,2022,2025,2028],{"className":1979},[607],[574,1981],{"className":1982,"style":702},[611],[574,1984,1850],{"className":1985},[1555],[574,1987,667],{"className":1988},[710],[574,1990,1992],{"className":1991},[616],"6",[574,1994,1996,1999],{"className":1995},[616],[574,1997,893],{"className":1998},[616],[574,2000,2002],{"className":2001},[897],[574,2003,2005],{"className":2004},[901],[574,2006,2008],{"className":2007},[905],[574,2009,2011],{"className":2010,"style":1551},[909],[574,2012,2013,2016],{"style":1584},[574,2014],{"className":2015,"style":917},[916],[574,2017,2019],{"className":2018},[921,922,923,924],[574,2020,869],{"className":2021},[722,924],[574,2023],{"className":2024,"style":718},[717],[574,2026,1857],{"className":2027},[722],[574,2029],{"className":2030,"style":718},[717],[574,2032,2034,2037,2040,2069,2072,2075,2078],{"className":2033},[607],[574,2035],{"className":2036,"style":702},[611],[574,2038,886],{"className":2039},[616],[574,2041,2043,2046],{"className":2042},[616],[574,2044,893],{"className":2045},[616],[574,2047,2049],{"className":2048},[897],[574,2050,2052],{"className":2051},[901],[574,2053,2055],{"className":2054},[905],[574,2056,2058],{"className":2057,"style":1551},[909],[574,2059,2060,2063],{"style":1584},[574,2061],{"className":2062,"style":917},[916],[574,2064,2066],{"className":2065},[921,922,923,924],[574,2067,869],{"className":2068},[722,924],[574,2070,678],{"className":2071},[738],[574,2073],{"className":2074,"style":742},[717],[574,2076,681],{"className":2077},[746],[574,2079],{"className":2080,"style":742},[717],[574,2082,2084,2087,2090,2093,2096,2125,2128,2131],{"className":2083},[607],[574,2085],{"className":2086,"style":1551},[611],[574,2088,1850],{"className":2089},[1555],[574,2091],{"className":2092,"style":1559},[717],[574,2094,1992],{"className":2095},[616],[574,2097,2099,2102],{"className":2098},[616],[574,2100,893],{"className":2101},[616],[574,2103,2105],{"className":2104},[897],[574,2106,2108],{"className":2107},[901],[574,2109,2111],{"className":2110},[905],[574,2112,2114],{"className":2113,"style":1551},[909],[574,2115,2116,2119],{"style":1584},[574,2117],{"className":2118,"style":917},[916],[574,2120,2122],{"className":2121},[921,922,923,924],[574,2123,869],{"className":2124},[722,924],[574,2126],{"className":2127,"style":742},[717],[574,2129,681],{"className":2130},[746],[574,2132],{"className":2133,"style":742},[717],[574,2135,2137,2140],{"className":2136},[607],[574,2138],{"className":2139,"style":1766},[611],[574,2141,2143,2146,2199],{"className":2142},[616],[574,2144],{"className":2145},[710,1111],[574,2147,2149],{"className":2148},[1079],[574,2150,2152,2191],{"className":2151},[901,1118],[574,2153,2155,2188],{"className":2154},[905],[574,2156,2158,2169,2177],{"className":2157,"style":1785},[909],[574,2159,2160,2163],{"style":1788},[574,2161],{"className":2162,"style":1132},[916],[574,2164,2166],{"className":2165},[616],[574,2167,824],{"className":2168},[616],[574,2170,2171,2174],{"style":1144},[574,2172],{"className":2173,"style":1132},[916],[574,2175],{"className":2176,"style":1152},[1151],[574,2178,2179,2182],{"style":1808},[574,2180],{"className":2181,"style":1132},[916],[574,2183,2185],{"className":2184},[616],[574,2186,1536],{"className":2187},[616],[574,2189,1172],{"className":2190},[1171],[574,2192,2194],{"className":2193},[905],[574,2195,2197],{"className":2196,"style":1827},[909],[574,2198],{},[574,2200],{"className":2201},[738,1111],[574,2203,2205],{"className":2204},[1466],[574,2206,2208,2273],{"className":2207},[577],[574,2209,2211],{"className":2210},[581],[583,2212,2213],{"xmlns":585,"display":1475},[587,2214,2215,2270],{},[590,2216,2217,2220,2222,2229,2231,2233,2235,2237,2244,2246,2252,2254,2256,2258,2260,2266,2268],{},[593,2218,2219],{},"tan",[664,2221,1485],{},[862,2223,2224,2227],{},[822,2225,2226],{},"225",[664,2228,869],{},[664,2230,681],{},[593,2232,2219],{},[664,2234,1485],{},[664,2236,667],{"stretchy":666},[862,2238,2239,2242],{},[822,2240,2241],{},"45",[664,2243,869],{},[664,2245,673],{},[862,2247,2248,2250],{},[822,2249,982],{},[664,2251,869],{},[664,2253,678],{"stretchy":666},[664,2255,681],{},[593,2257,2219],{},[664,2259,1485],{},[862,2261,2262,2264],{},[822,2263,2241],{},[664,2265,869],{},[664,2267,681],{},[822,2269,1536],{},[596,2271,2272],{"encoding":598},"\\tan 225^\\circ = \\tan(45^\\circ + 180^\\circ) = \\tan 45^\\circ = 1",[574,2274,2276,2331,2385,2435,2488],{"className":2275,"ariaHidden":603},[602],[574,2277,2279,2282,2285,2288,2292,2322,2325,2328],{"className":2278},[607],[574,2280],{"className":2281,"style":1551},[611],[574,2283,2219],{"className":2284},[1555],[574,2286],{"className":2287,"style":1559},[717],[574,2289,2291],{"className":2290},[616],"22",[574,2293,2295,2299],{"className":2294},[616],[574,2296,2298],{"className":2297},[616],"5",[574,2300,2302],{"className":2301},[897],[574,2303,2305],{"className":2304},[901],[574,2306,2308],{"className":2307},[905],[574,2309,2311],{"className":2310,"style":1551},[909],[574,2312,2313,2316],{"style":1584},[574,2314],{"className":2315,"style":917},[916],[574,2317,2319],{"className":2318},[921,922,923,924],[574,2320,869],{"className":2321},[722,924],[574,2323],{"className":2324,"style":742},[717],[574,2326,681],{"className":2327},[746],[574,2329],{"className":2330,"style":742},[717],[574,2332,2334,2337,2340,2343,2347,2376,2379,2382],{"className":2333},[607],[574,2335],{"className":2336,"style":702},[611],[574,2338,2219],{"className":2339},[1555],[574,2341,667],{"className":2342},[710],[574,2344,2346],{"className":2345},[616],"4",[574,2348,2350,2353],{"className":2349},[616],[574,2351,2298],{"className":2352},[616],[574,2354,2356],{"className":2355},[897],[574,2357,2359],{"className":2358},[901],[574,2360,2362],{"className":2361},[905],[574,2363,2365],{"className":2364,"style":1551},[909],[574,2366,2367,2370],{"style":1584},[574,2368],{"className":2369,"style":917},[916],[574,2371,2373],{"className":2372},[921,922,923,924],[574,2374,869],{"className":2375},[722,924],[574,2377],{"className":2378,"style":718},[717],[574,2380,673],{"className":2381},[722],[574,2383],{"className":2384,"style":718},[717],[574,2386,2388,2391,2394,2423,2426,2429,2432],{"className":2387},[607],[574,2389],{"className":2390,"style":702},[611],[574,2392,1000],{"className":2393},[616],[574,2395,2397,2400],{"className":2396},[616],[574,2398,893],{"className":2399},[616],[574,2401,2403],{"className":2402},[897],[574,2404,2406],{"className":2405},[901],[574,2407,2409],{"className":2408},[905],[574,2410,2412],{"className":2411,"style":1551},[909],[574,2413,2414,2417],{"style":1584},[574,2415],{"className":2416,"style":917},[916],[574,2418,2420],{"className":2419},[921,922,923,924],[574,2421,869],{"className":2422},[722,924],[574,2424,678],{"className":2425},[738],[574,2427],{"className":2428,"style":742},[717],[574,2430,681],{"className":2431},[746],[574,2433],{"className":2434,"style":742},[717],[574,2436,2438,2441,2444,2447,2450,2479,2482,2485],{"className":2437},[607],[574,2439],{"className":2440,"style":1551},[611],[574,2442,2219],{"className":2443},[1555],[574,2445],{"className":2446,"style":1559},[717],[574,2448,2346],{"className":2449},[616],[574,2451,2453,2456],{"className":2452},[616],[574,2454,2298],{"className":2455},[616],[574,2457,2459],{"className":2458},[897],[574,2460,2462],{"className":2461},[901],[574,2463,2465],{"className":2464},[905],[574,2466,2468],{"className":2467,"style":1551},[909],[574,2469,2470,2473],{"style":1584},[574,2471],{"className":2472,"style":917},[916],[574,2474,2476],{"className":2475},[921,922,923,924],[574,2477,869],{"className":2478},[722,924],[574,2480],{"className":2481,"style":742},[717],[574,2483,681],{"className":2484},[746],[574,2486],{"className":2487,"style":742},[717],[574,2489,2491,2494],{"className":2490},[607],[574,2492],{"className":2493,"style":840},[611],[574,2495,1536],{"className":2496},[616],[565,2498,2499,2500,2698,2699,798],{},"Großer Winkel: ",[574,2501,2503,2543],{"className":2502},[577],[574,2504,2506],{"className":2505},[581],[583,2507,2508],{"xmlns":585},[587,2509,2510,2540],{},[590,2511,2512,2519,2521,2523,2526,2532,2534],{},[862,2513,2514,2517],{},[822,2515,2516],{},"1110",[664,2518,869],{},[664,2520,1857],{},[822,2522,1618],{},[664,2524,2525],{},"⋅",[862,2527,2528,2530],{},[822,2529,866],{},[664,2531,869],{},[664,2533,681],{},[862,2535,2536,2538],{},[822,2537,1505],{},[664,2539,869],{},[596,2541,2542],{"encoding":598},"1110^\\circ - 3 \\cdot 360^\\circ = 30^\\circ",[574,2544,2546,2595,2613,2660],{"className":2545,"ariaHidden":603},[602],[574,2547,2549,2553,2557,2586,2589,2592],{"className":2548},[607],[574,2550],{"className":2551,"style":2552},[611],"height:0.7574em;vertical-align:-0.0833em;",[574,2554,2556],{"className":2555},[616],"111",[574,2558,2560,2563],{"className":2559},[616],[574,2561,893],{"className":2562},[616],[574,2564,2566],{"className":2565},[897],[574,2567,2569],{"className":2568},[901],[574,2570,2572],{"className":2571},[905],[574,2573,2575],{"className":2574,"style":882},[909],[574,2576,2577,2580],{"style":912},[574,2578],{"className":2579,"style":917},[916],[574,2581,2583],{"className":2582},[921,922,923,924],[574,2584,869],{"className":2585},[722,924],[574,2587],{"className":2588,"style":718},[717],[574,2590,1857],{"className":2591},[722],[574,2593],{"className":2594,"style":718},[717],[574,2596,2598,2601,2604,2607,2610],{"className":2597},[607],[574,2599],{"className":2600,"style":840},[611],[574,2602,1618],{"className":2603},[616],[574,2605],{"className":2606,"style":718},[717],[574,2608,2525],{"className":2609},[722],[574,2611],{"className":2612,"style":718},[717],[574,2614,2616,2619,2622,2651,2654,2657],{"className":2615},[607],[574,2617],{"className":2618,"style":882},[611],[574,2620,886],{"className":2621},[616],[574,2623,2625,2628],{"className":2624},[616],[574,2626,893],{"className":2627},[616],[574,2629,2631],{"className":2630},[897],[574,2632,2634],{"className":2633},[901],[574,2635,2637],{"className":2636},[905],[574,2638,2640],{"className":2639,"style":882},[909],[574,2641,2642,2645],{"style":912},[574,2643],{"className":2644,"style":917},[916],[574,2646,2648],{"className":2647},[921,922,923,924],[574,2649,869],{"className":2650},[722,924],[574,2652],{"className":2653,"style":742},[717],[574,2655,681],{"className":2656},[746],[574,2658],{"className":2659,"style":742},[717],[574,2661,2663,2666,2669],{"className":2662},[607],[574,2664],{"className":2665,"style":882},[611],[574,2667,1618],{"className":2668},[616],[574,2670,2672,2675],{"className":2671},[616],[574,2673,893],{"className":2674},[616],[574,2676,2678],{"className":2677},[897],[574,2679,2681],{"className":2680},[901],[574,2682,2684],{"className":2683},[905],[574,2685,2687],{"className":2686,"style":882},[909],[574,2688,2689,2692],{"style":912},[574,2690],{"className":2691,"style":917},[916],[574,2693,2695],{"className":2694},[921,922,923,924],[574,2696,869],{"className":2697},[722,924],", also ",[574,2700,2702,2744],{"className":2701},[577],[574,2703,2705],{"className":2704},[581],[583,2706,2707],{"xmlns":585},[587,2708,2709,2741],{},[590,2710,2711,2713,2715,2721,2723,2725,2727,2733,2735],{},[593,2712,1482],{},[664,2714,1485],{},[862,2716,2717,2719],{},[822,2718,2516],{},[664,2720,869],{},[664,2722,681],{},[593,2724,1482],{},[664,2726,1485],{},[862,2728,2729,2731],{},[822,2730,1505],{},[664,2732,869],{},[664,2734,681],{},[1079,2736,2737,2739],{},[822,2738,1536],{},[822,2740,824],{},[596,2742,2743],{"encoding":598},"\\sin 1110^\\circ = \\sin 30^\\circ = \\frac{1}{2}",[574,2745,2747,2800,2853],{"className":2746,"ariaHidden":603},[602],[574,2748,2750,2753,2756,2759,2762,2791,2794,2797],{"className":2749},[607],[574,2751],{"className":2752,"style":882},[611],[574,2754,1482],{"className":2755},[1555],[574,2757],{"className":2758,"style":1559},[717],[574,2760,2556],{"className":2761},[616],[574,2763,2765,2768],{"className":2764},[616],[574,2766,893],{"className":2767},[616],[574,2769,2771],{"className":2770},[897],[574,2772,2774],{"className":2773},[901],[574,2775,2777],{"className":2776},[905],[574,2778,2780],{"className":2779,"style":882},[909],[574,2781,2782,2785],{"style":912},[574,2783],{"className":2784,"style":917},[916],[574,2786,2788],{"className":2787},[921,922,923,924],[574,2789,869],{"className":2790},[722,924],[574,2792],{"className":2793,"style":742},[717],[574,2795,681],{"className":2796},[746],[574,2798],{"className":2799,"style":742},[717],[574,2801,2803,2806,2809,2812,2815,2844,2847,2850],{"className":2802},[607],[574,2804],{"className":2805,"style":882},[611],[574,2807,1482],{"className":2808},[1555],[574,2810],{"className":2811,"style":1559},[717],[574,2813,1618],{"className":2814},[616],[574,2816,2818,2821],{"className":2817},[616],[574,2819,893],{"className":2820},[616],[574,2822,2824],{"className":2823},[897],[574,2825,2827],{"className":2826},[901],[574,2828,2830],{"className":2829},[905],[574,2831,2833],{"className":2832,"style":882},[909],[574,2834,2835,2838],{"style":912},[574,2836],{"className":2837,"style":917},[916],[574,2839,2841],{"className":2840},[921,922,923,924],[574,2842,869],{"className":2843},[722,924],[574,2845],{"className":2846,"style":742},[717],[574,2848,681],{"className":2849},[746],[574,2851],{"className":2852,"style":742},[717],[574,2854,2856,2860],{"className":2855},[607],[574,2857],{"className":2858,"style":2859},[611],"height:1.1901em;vertical-align:-0.345em;",[574,2861,2863,2866,2926],{"className":2862},[616],[574,2864],{"className":2865},[710,1111],[574,2867,2869],{"className":2868},[1079],[574,2870,2872,2918],{"className":2871},[901,1118],[574,2873,2875,2915],{"className":2874},[905],[574,2876,2879,2893,2901],{"className":2877,"style":2878},[909],"height:0.8451em;",[574,2880,2881,2884],{"style":1128},[574,2882],{"className":2883,"style":1132},[916],[574,2885,2887],{"className":2886},[921,922,923,924],[574,2888,2890],{"className":2889},[616,924],[574,2891,824],{"className":2892},[616,924],[574,2894,2895,2898],{"style":1144},[574,2896],{"className":2897,"style":1132},[916],[574,2899],{"className":2900,"style":1152},[1151],[574,2902,2903,2906],{"style":1155},[574,2904],{"className":2905,"style":1132},[916],[574,2907,2909],{"className":2908},[921,922,923,924],[574,2910,2912],{"className":2911},[616,924],[574,2913,1536],{"className":2914},[616,924],[574,2916,1172],{"className":2917},[1171],[574,2919,2921],{"className":2920},[905],[574,2922,2924],{"className":2923,"style":1179},[909],[574,2925],{},[574,2927],{"className":2928},[738,1111],[560,2930,2932],{"id":2931},"typische-fehler","Typische Fehler",[800,2934,2935,3342,3857,4064],{},[803,2936,2937,2938,2971,2972,3000,3001,3063,3064,3211,3212,798],{},"Beim Tangens mit ",[574,2939,2941,2956],{"className":2940},[577],[574,2942,2944],{"className":2943},[581],[583,2945,2946],{"xmlns":585},[587,2947,2948,2954],{},[590,2949,2950,2952],{},[822,2951,824],{},[593,2953,827],{},[596,2955,830],{"encoding":598},[574,2957,2959],{"className":2958,"ariaHidden":603},[602],[574,2960,2962,2965,2968],{"className":2961},[607],[574,2963],{"className":2964,"style":840},[611],[574,2966,824],{"className":2967},[616],[574,2969,827],{"className":2970,"style":847},[616,617]," statt ",[574,2973,2975,2988],{"className":2974},[577],[574,2976,2978],{"className":2977},[581],[583,2979,2980],{"xmlns":585},[587,2981,2982,2986],{},[590,2983,2984],{},[593,2985,827],{},[596,2987,952],{"encoding":598},[574,2989,2991],{"className":2990,"ariaHidden":603},[602],[574,2992,2994,2997],{"className":2993},[607],[574,2995],{"className":2996,"style":794},[611],[574,2998,827],{"className":2999,"style":847},[616,617]," rechnen. Das ist nicht falsch, verschenkt aber Lösungen: ",[574,3002,3004,3026],{"className":3003},[577],[574,3005,3007],{"className":3006},[581],[583,3008,3009],{"xmlns":585},[587,3010,3011,3023],{},[590,3012,3013,3015,3017,3019,3021],{},[593,3014,2219],{},[664,3016,1485],{},[593,3018,670],{},[664,3020,681],{},[822,3022,1536],{},[596,3024,3025],{"encoding":598},"\\tan x = 1",[574,3027,3029,3054],{"className":3028,"ariaHidden":603},[602],[574,3030,3032,3036,3039,3042,3045,3048,3051],{"className":3031},[607],[574,3033],{"className":3034,"style":3035},[611],"height:0.6151em;",[574,3037,2219],{"className":3038},[1555],[574,3040],{"className":3041,"style":1559},[717],[574,3043,670],{"className":3044},[616,617],[574,3046],{"className":3047,"style":742},[717],[574,3049,681],{"className":3050},[746],[574,3052],{"className":3053,"style":742},[717],[574,3055,3057,3060],{"className":3056},[607],[574,3058],{"className":3059,"style":840},[611],[574,3061,1536],{"className":3062},[616]," hat die Lösungen ",[574,3065,3067,3095],{"className":3066},[577],[574,3068,3070],{"className":3069},[581],[583,3071,3072],{"xmlns":585},[587,3073,3074,3092],{},[590,3075,3076,3078,3080,3086,3088,3090],{},[593,3077,670],{},[664,3079,681],{},[1079,3081,3082,3084],{},[593,3083,827],{},[822,3085,2346],{},[664,3087,673],{},[593,3089,1048],{},[593,3091,827],{},[596,3093,3094],{"encoding":598},"x = \\frac{\\pi}{4} + k\\pi",[574,3096,3098,3116,3199],{"className":3097,"ariaHidden":603},[602],[574,3099,3101,3104,3107,3110,3113],{"className":3100},[607],[574,3102],{"className":3103,"style":794},[611],[574,3105,670],{"className":3106},[616,617],[574,3108],{"className":3109,"style":742},[717],[574,3111,681],{"className":3112},[746],[574,3114],{"className":3115,"style":742},[717],[574,3117,3119,3122,3190,3193,3196],{"className":3118},[607],[574,3120],{"className":3121,"style":1104},[611],[574,3123,3125,3128,3187],{"className":3124},[616],[574,3126],{"className":3127},[710,1111],[574,3129,3131],{"className":3130},[1079],[574,3132,3134,3179],{"className":3133},[901,1118],[574,3135,3137,3176],{"className":3136},[905],[574,3138,3140,3154,3162],{"className":3139,"style":1125},[909],[574,3141,3142,3145],{"style":1128},[574,3143],{"className":3144,"style":1132},[916],[574,3146,3148],{"className":3147},[921,922,923,924],[574,3149,3151],{"className":3150},[616,924],[574,3152,2346],{"className":3153},[616,924],[574,3155,3156,3159],{"style":1144},[574,3157],{"className":3158,"style":1132},[916],[574,3160],{"className":3161,"style":1152},[1151],[574,3163,3164,3167],{"style":1155},[574,3165],{"className":3166,"style":1132},[916],[574,3168,3170],{"className":3169},[921,922,923,924],[574,3171,3173],{"className":3172},[616,924],[574,3174,827],{"className":3175,"style":847},[616,617,924],[574,3177,1172],{"className":3178},[1171],[574,3180,3182],{"className":3181},[905],[574,3183,3185],{"className":3184,"style":1179},[909],[574,3186],{},[574,3188],{"className":3189},[738,1111],[574,3191],{"className":3192,"style":718},[717],[574,3194,673],{"className":3195},[722],[574,3197],{"className":3198,"style":718},[717],[574,3200,3202,3205,3208],{"className":3201},[607],[574,3203],{"className":3204,"style":1060},[611],[574,3206,1048],{"className":3207,"style":1064},[616,617],[574,3209,827],{"className":3210,"style":847},[616,617],", nicht nur ",[574,3213,3215,3241],{"className":3214},[577],[574,3216,3218],{"className":3217},[581],[583,3219,3220],{"xmlns":585},[587,3221,3222,3238],{},[590,3223,3224,3230,3232,3234,3236],{},[1079,3225,3226,3228],{},[593,3227,827],{},[822,3229,2346],{},[664,3231,673],{},[822,3233,824],{},[593,3235,1048],{},[593,3237,827],{},[596,3239,3240],{"encoding":598},"\\frac{\\pi}{4} + 2k\\pi",[574,3242,3244,3327],{"className":3243,"ariaHidden":603},[602],[574,3245,3247,3250,3318,3321,3324],{"className":3246},[607],[574,3248],{"className":3249,"style":1104},[611],[574,3251,3253,3256,3315],{"className":3252},[616],[574,3254],{"className":3255},[710,1111],[574,3257,3259],{"className":3258},[1079],[574,3260,3262,3307],{"className":3261},[901,1118],[574,3263,3265,3304],{"className":3264},[905],[574,3266,3268,3282,3290],{"className":3267,"style":1125},[909],[574,3269,3270,3273],{"style":1128},[574,3271],{"className":3272,"style":1132},[916],[574,3274,3276],{"className":3275},[921,922,923,924],[574,3277,3279],{"className":3278},[616,924],[574,3280,2346],{"className":3281},[616,924],[574,3283,3284,3287],{"style":1144},[574,3285],{"className":3286,"style":1132},[916],[574,3288],{"className":3289,"style":1152},[1151],[574,3291,3292,3295],{"style":1155},[574,3293],{"className":3294,"style":1132},[916],[574,3296,3298],{"className":3297},[921,922,923,924],[574,3299,3301],{"className":3300},[616,924],[574,3302,827],{"className":3303,"style":847},[616,617,924],[574,3305,1172],{"className":3306},[1171],[574,3308,3310],{"className":3309},[905],[574,3311,3313],{"className":3312,"style":1179},[909],[574,3314],{},[574,3316],{"className":3317},[738,1111],[574,3319],{"className":3320,"style":718},[717],[574,3322,673],{"className":3323},[722],[574,3325],{"className":3326,"style":718},[717],[574,3328,3330,3333,3336,3339],{"className":3329},[607],[574,3331],{"className":3332,"style":1060},[611],[574,3334,824],{"className":3335},[616],[574,3337,1048],{"className":3338,"style":1064},[616,617],[574,3340,827],{"className":3341,"style":847},[616,617],[803,3343,3344,3345,3443,3444,798],{},"Die Periode des Tangens für ",[574,3346,3348,3366],{"className":3347},[577],[574,3349,3351],{"className":3350},[581],[583,3352,3353],{"xmlns":585},[587,3354,3355,3363],{},[590,3356,3357],{},[1079,3358,3359,3361],{},[593,3360,827],{},[822,3362,824],{},[596,3364,3365],{"encoding":598},"\\frac{\\pi}{2}",[574,3367,3369],{"className":3368,"ariaHidden":603},[602],[574,3370,3372,3375],{"className":3371},[607],[574,3373],{"className":3374,"style":1104},[611],[574,3376,3378,3381,3440],{"className":3377},[616],[574,3379],{"className":3380},[710,1111],[574,3382,3384],{"className":3383},[1079],[574,3385,3387,3432],{"className":3386},[901,1118],[574,3388,3390,3429],{"className":3389},[905],[574,3391,3393,3407,3415],{"className":3392,"style":1125},[909],[574,3394,3395,3398],{"style":1128},[574,3396],{"className":3397,"style":1132},[916],[574,3399,3401],{"className":3400},[921,922,923,924],[574,3402,3404],{"className":3403},[616,924],[574,3405,824],{"className":3406},[616,924],[574,3408,3409,3412],{"style":1144},[574,3410],{"className":3411,"style":1132},[916],[574,3413],{"className":3414,"style":1152},[1151],[574,3416,3417,3420],{"style":1155},[574,3418],{"className":3419,"style":1132},[916],[574,3421,3423],{"className":3422},[921,922,923,924],[574,3424,3426],{"className":3425},[616,924],[574,3427,827],{"className":3428,"style":847},[616,617,924],[574,3430,1172],{"className":3431},[1171],[574,3433,3435],{"className":3434},[905],[574,3436,3438],{"className":3437,"style":1179},[909],[574,3439],{},[574,3441],{"className":3442},[738,1111]," halten. Es ist ",[574,3445,3447,3507],{"className":3446},[577],[574,3448,3450],{"className":3449},[581],[583,3451,3452],{"xmlns":585},[587,3453,3454,3504],{},[590,3455,3456,3458,3460,3480,3482,3484,3486,3490,3492,3494,3500,3502],{},[593,3457,2219],{},[664,3459,1485],{},[590,3461,3462,3464,3470,3472,3478],{},[664,3463,667],{"fence":603},[1079,3465,3466,3468],{},[593,3467,827],{},[822,3469,2346],{},[664,3471,673],{},[1079,3473,3474,3476],{},[593,3475,827],{},[822,3477,824],{},[664,3479,678],{"fence":603},[664,3481,681],{},[664,3483,1857],{},[822,3485,1536],{},[664,3487,3489],{"mathvariant":3488},"normal","≠",[593,3491,2219],{},[664,3493,1485],{},[1079,3495,3496,3498],{},[593,3497,827],{},[822,3499,2346],{},[664,3501,681],{},[822,3503,1536],{},[596,3505,3506],{"encoding":598},"\\tan\\left(\\frac{\\pi}{4} + \\frac{\\pi}{2}\\right) = -1 \\neq \\tan \\frac{\\pi}{4} = 1",[574,3508,3510,3697,3759,3848],{"className":3509,"ariaHidden":603},[602],[574,3511,3513,3517,3520,3523,3688,3691,3694],{"className":3512},[607],[574,3514],{"className":3515,"style":3516},[611],"height:1.2em;vertical-align:-0.35em;",[574,3518,2219],{"className":3519},[1555],[574,3521],{"className":3522,"style":1559},[717],[574,3524,3527,3537,3605,3608,3611,3614,3682],{"className":3525},[3526],"minner",[574,3528,3532],{"className":3529,"style":3531},[710,3530],"delimcenter","top:0em;",[574,3533,667],{"className":3534},[3535,3536],"delimsizing","size1",[574,3538,3540,3543,3602],{"className":3539},[616],[574,3541],{"className":3542},[710,1111],[574,3544,3546],{"className":3545},[1079],[574,3547,3549,3594],{"className":3548},[901,1118],[574,3550,3552,3591],{"className":3551},[905],[574,3553,3555,3569,3577],{"className":3554,"style":1125},[909],[574,3556,3557,3560],{"style":1128},[574,3558],{"className":3559,"style":1132},[916],[574,3561,3563],{"className":3562},[921,922,923,924],[574,3564,3566],{"className":3565},[616,924],[574,3567,2346],{"className":3568},[616,924],[574,3570,3571,3574],{"style":1144},[574,3572],{"className":3573,"style":1132},[916],[574,3575],{"className":3576,"style":1152},[1151],[574,3578,3579,3582],{"style":1155},[574,3580],{"className":3581,"style":1132},[916],[574,3583,3585],{"className":3584},[921,922,923,924],[574,3586,3588],{"className":3587},[616,924],[574,3589,827],{"className":3590,"style":847},[616,617,924],[574,3592,1172],{"className":3593},[1171],[574,3595,3597],{"className":3596},[905],[574,3598,3600],{"className":3599,"style":1179},[909],[574,3601],{},[574,3603],{"className":3604},[738,1111],[574,3606],{"className":3607,"style":718},[717],[574,3609,673],{"className":3610},[722],[574,3612],{"className":3613,"style":718},[717],[574,3615,3617,3620,3679],{"className":3616},[616],[574,3618],{"className":3619},[710,1111],[574,3621,3623],{"className":3622},[1079],[574,3624,3626,3671],{"className":3625},[901,1118],[574,3627,3629,3668],{"className":3628},[905],[574,3630,3632,3646,3654],{"className":3631,"style":1125},[909],[574,3633,3634,3637],{"style":1128},[574,3635],{"className":3636,"style":1132},[916],[574,3638,3640],{"className":3639},[921,922,923,924],[574,3641,3643],{"className":3642},[616,924],[574,3644,824],{"className":3645},[616,924],[574,3647,3648,3651],{"style":1144},[574,3649],{"className":3650,"style":1132},[916],[574,3652],{"className":3653,"style":1152},[1151],[574,3655,3656,3659],{"style":1155},[574,3657],{"className":3658,"style":1132},[916],[574,3660,3662],{"className":3661},[921,922,923,924],[574,3663,3665],{"className":3664},[616,924],[574,3666,827],{"className":3667,"style":847},[616,617,924],[574,3669,1172],{"className":3670},[1171],[574,3672,3674],{"className":3673},[905],[574,3675,3677],{"className":3676,"style":1179},[909],[574,3678],{},[574,3680],{"className":3681},[738,1111],[574,3683,3685],{"className":3684,"style":3531},[738,3530],[574,3686,678],{"className":3687},[3535,3536],[574,3689],{"className":3690,"style":742},[717],[574,3692,681],{"className":3693},[746],[574,3695],{"className":3696,"style":742},[717],[574,3698,3700,3704,3707,3710,3713,3756],{"className":3699},[607],[574,3701],{"className":3702,"style":3703},[611],"height:0.8889em;vertical-align:-0.1944em;",[574,3705,1857],{"className":3706},[616],[574,3708,1536],{"className":3709},[616],[574,3711],{"className":3712,"style":742},[717],[574,3714,3716,3749,3753],{"className":3715},[746],[574,3717,3719],{"className":3718},[746],[574,3720,3723],{"className":3721},[616,3722],"vbox",[574,3724,3727],{"className":3725},[3726],"thinbox",[574,3728,3731,3734,3745],{"className":3729},[3730],"rlap",[574,3732],{"className":3733,"style":3703},[611],[574,3735,3738],{"className":3736},[3737],"inner",[574,3739,3741],{"className":3740},[616],[574,3742,3744],{"className":3743},[746],"",[574,3746],{"className":3747},[3748],"fix",[574,3750],{"className":3751},[717,3752],"nobreak",[574,3754,681],{"className":3755},[746],[574,3757],{"className":3758,"style":742},[717],[574,3760,3762,3765,3768,3771,3839,3842,3845],{"className":3761},[607],[574,3763],{"className":3764,"style":1104},[611],[574,3766,2219],{"className":3767},[1555],[574,3769],{"className":3770,"style":1559},[717],[574,3772,3774,3777,3836],{"className":3773},[616],[574,3775],{"className":3776},[710,1111],[574,3778,3780],{"className":3779},[1079],[574,3781,3783,3828],{"className":3782},[901,1118],[574,3784,3786,3825],{"className":3785},[905],[574,3787,3789,3803,3811],{"className":3788,"style":1125},[909],[574,3790,3791,3794],{"style":1128},[574,3792],{"className":3793,"style":1132},[916],[574,3795,3797],{"className":3796},[921,922,923,924],[574,3798,3800],{"className":3799},[616,924],[574,3801,2346],{"className":3802},[616,924],[574,3804,3805,3808],{"style":1144},[574,3806],{"className":3807,"style":1132},[916],[574,3809],{"className":3810,"style":1152},[1151],[574,3812,3813,3816],{"style":1155},[574,3814],{"className":3815,"style":1132},[916],[574,3817,3819],{"className":3818},[921,922,923,924],[574,3820,3822],{"className":3821},[616,924],[574,3823,827],{"className":3824,"style":847},[616,617,924],[574,3826,1172],{"className":3827},[1171],[574,3829,3831],{"className":3830},[905],[574,3832,3834],{"className":3833,"style":1179},[909],[574,3835],{},[574,3837],{"className":3838},[738,1111],[574,3840],{"className":3841,"style":742},[717],[574,3843,681],{"className":3844},[746],[574,3846],{"className":3847,"style":742},[717],[574,3849,3851,3854],{"className":3850},[607],[574,3852],{"className":3853,"style":840},[611],[574,3855,1536],{"className":3856},[616],[803,3858,3859,3860,3921,3922,2971,3990,4063],{},"Die Periode ",[574,3861,3863,3880],{"className":3862},[577],[574,3864,3866],{"className":3865},[581],[583,3867,3868],{"xmlns":585},[587,3869,3870,3878],{},[590,3871,3872],{},[862,3873,3874,3876],{},[822,3875,866],{},[664,3877,869],{},[596,3879,872],{"encoding":598},[574,3881,3883],{"className":3882,"ariaHidden":603},[602],[574,3884,3886,3889,3892],{"className":3885},[607],[574,3887],{"className":3888,"style":882},[611],[574,3890,886],{"className":3891},[616],[574,3893,3895,3898],{"className":3894},[616],[574,3896,893],{"className":3897},[616],[574,3899,3901],{"className":3900},[897],[574,3902,3904],{"className":3903},[901],[574,3905,3907],{"className":3906},[905],[574,3908,3910],{"className":3909,"style":882},[909],[574,3911,3912,3915],{"style":912},[574,3913],{"className":3914,"style":917},[916],[574,3916,3918],{"className":3917},[921,922,923,924],[574,3919,869],{"className":3920},[722,924]," im Bogenmaß verwenden, also ",[574,3923,3925,3951],{"className":3924},[577],[574,3926,3928],{"className":3927},[581],[583,3929,3930],{"xmlns":585},[587,3931,3932,3948],{},[590,3933,3934,3936,3938,3940,3942,3944,3946],{},[593,3935,1482],{},[664,3937,1485],{},[664,3939,667],{"stretchy":666},[593,3941,670],{},[664,3943,673],{},[822,3945,866],{},[664,3947,678],{"stretchy":666},[596,3949,3950],{"encoding":598},"\\sin(x + 360)",[574,3952,3954,3978],{"className":3953,"ariaHidden":603},[602],[574,3955,3957,3960,3963,3966,3969,3972,3975],{"className":3956},[607],[574,3958],{"className":3959,"style":702},[611],[574,3961,1482],{"className":3962},[1555],[574,3964,667],{"className":3965},[710],[574,3967,670],{"className":3968},[616,617],[574,3970],{"className":3971,"style":718},[717],[574,3973,673],{"className":3974},[722],[574,3976],{"className":3977,"style":718},[717],[574,3979,3981,3984,3987],{"className":3980},[607],[574,3982],{"className":3983,"style":702},[611],[574,3985,866],{"className":3986},[616],[574,3988,678],{"className":3989},[738],[574,3991,3993,4021],{"className":3992},[577],[574,3994,3996],{"className":3995},[581],[583,3997,3998],{"xmlns":585},[587,3999,4000,4018],{},[590,4001,4002,4004,4006,4008,4010,4012,4014,4016],{},[593,4003,1482],{},[664,4005,1485],{},[664,4007,667],{"stretchy":666},[593,4009,670],{},[664,4011,673],{},[822,4013,824],{},[593,4015,827],{},[664,4017,678],{"stretchy":666},[596,4019,4020],{"encoding":598},"\\sin(x + 2\\pi)",[574,4022,4024,4048],{"className":4023,"ariaHidden":603},[602],[574,4025,4027,4030,4033,4036,4039,4042,4045],{"className":4026},[607],[574,4028],{"className":4029,"style":702},[611],[574,4031,1482],{"className":4032},[1555],[574,4034,667],{"className":4035},[710],[574,4037,670],{"className":4038},[616,617],[574,4040],{"className":4041,"style":718},[717],[574,4043,673],{"className":4044},[722],[574,4046],{"className":4047,"style":718},[717],[574,4049,4051,4054,4057,4060],{"className":4050},[607],[574,4052],{"className":4053,"style":702},[611],[574,4055,824],{"className":4056},[616],[574,4058,827],{"className":4059,"style":847},[616,617],[574,4061,678],{"className":4062},[738]," schreiben.",[803,4065,4066,4067,4168,4169,798],{},"Annehmen, ",[574,4068,4070,4104],{"className":4069},[577],[574,4071,4073],{"className":4072},[581],[583,4074,4075],{"xmlns":585},[587,4076,4077,4101],{},[590,4078,4079,4081,4083,4085,4087,4089,4091,4093,4095,4097,4099],{},[593,4080,1482],{},[664,4082,1485],{},[664,4084,667],{"stretchy":666},[593,4086,670],{},[664,4088,673],{},[593,4090,827],{},[664,4092,678],{"stretchy":666},[664,4094,681],{},[593,4096,1482],{},[664,4098,1485],{},[593,4100,670],{},[596,4102,4103],{"encoding":598},"\\sin(x + \\pi) = \\sin x",[574,4105,4107,4131,4152],{"className":4106,"ariaHidden":603},[602],[574,4108,4110,4113,4116,4119,4122,4125,4128],{"className":4109},[607],[574,4111],{"className":4112,"style":702},[611],[574,4114,1482],{"className":4115},[1555],[574,4117,667],{"className":4118},[710],[574,4120,670],{"className":4121},[616,617],[574,4123],{"className":4124,"style":718},[717],[574,4126,673],{"className":4127},[722],[574,4129],{"className":4130,"style":718},[717],[574,4132,4134,4137,4140,4143,4146,4149],{"className":4133},[607],[574,4135],{"className":4136,"style":702},[611],[574,4138,827],{"className":4139,"style":847},[616,617],[574,4141,678],{"className":4142},[738],[574,4144],{"className":4145,"style":742},[717],[574,4147,681],{"className":4148},[746],[574,4150],{"className":4151,"style":742},[717],[574,4153,4155,4159,4162,4165],{"className":4154},[607],[574,4156],{"className":4157,"style":4158},[611],"height:0.6679em;",[574,4160,1482],{"className":4161},[1555],[574,4163],{"className":4164,"style":1559},[717],[574,4166,670],{"className":4167},[616,617],". Nach einer halben Periode wechselt das Vorzeichen: ",[574,4170,4172,4208],{"className":4171},[577],[574,4173,4175],{"className":4174},[581],[583,4176,4177],{"xmlns":585},[587,4178,4179,4205],{},[590,4180,4181,4183,4185,4187,4189,4191,4193,4195,4197,4199,4201,4203],{},[593,4182,1482],{},[664,4184,1485],{},[664,4186,667],{"stretchy":666},[593,4188,670],{},[664,4190,673],{},[593,4192,827],{},[664,4194,678],{"stretchy":666},[664,4196,681],{},[664,4198,1857],{},[593,4200,1482],{},[664,4202,1485],{},[593,4204,670],{},[596,4206,4207],{"encoding":598},"\\sin(x + \\pi) = -\\sin x",[574,4209,4211,4235,4256],{"className":4210,"ariaHidden":603},[602],[574,4212,4214,4217,4220,4223,4226,4229,4232],{"className":4213},[607],[574,4215],{"className":4216,"style":702},[611],[574,4218,1482],{"className":4219},[1555],[574,4221,667],{"className":4222},[710],[574,4224,670],{"className":4225},[616,617],[574,4227],{"className":4228,"style":718},[717],[574,4230,673],{"className":4231},[722],[574,4233],{"className":4234,"style":718},[717],[574,4236,4238,4241,4244,4247,4250,4253],{"className":4237},[607],[574,4239],{"className":4240,"style":702},[611],[574,4242,827],{"className":4243,"style":847},[616,617],[574,4245,678],{"className":4246},[738],[574,4248],{"className":4249,"style":742},[717],[574,4251,681],{"className":4252},[746],[574,4254],{"className":4255,"style":742},[717],[574,4257,4259,4263,4266,4269,4272,4275],{"className":4258},[607],[574,4260],{"className":4261,"style":4262},[611],"height:0.7512em;vertical-align:-0.0833em;",[574,4264,1857],{"className":4265},[616],[574,4267],{"className":4268,"style":1559},[717],[574,4270,1482],{"className":4271},[1555],[574,4273],{"className":4274,"style":1559},[717],[574,4276,670],{"className":4277},[616,617],{"title":4279,"searchDepth":4280,"depth":4280,"links":4281},"",2,[4282,4283,4284],{"id":562,"depth":4280,"text":563},{"id":1461,"depth":4280,"text":1462},{"id":2931,"depth":4280,"text":2932},[4286,4291,4296,4301,4304,4307,4310,4312,4314,4316,4318],{"lhs":4287,"rhs":4288,"where":4289},"sin(x + 2*k*pi)","sin(x)",{"k":4290},3,{"lhs":4292,"rhs":4293,"where":4294},"cos(x + 2*k*pi)","cos(x)",{"k":4295},-2,{"lhs":4297,"rhs":4298,"where":4299},"tan(x + k*pi)","tan(x)",{"k":4300},5,{"lhs":4302,"rhs":4303},"sin(x + pi)","-sin(x)",{"lhs":4305,"rhs":4306},"cos(x + pi)","-cos(x)",{"lhs":4308,"rhs":4309},"sin(390*pi\u002F180)","1\u002F2",{"lhs":4311,"rhs":4309},"cos(-300*pi\u002F180)",{"lhs":4313,"rhs":1536},"tan(225*pi\u002F180)",{"lhs":4315,"rhs":1505},"1110 - 3*360",{"lhs":4317,"rhs":4309},"sin(1110*pi\u002F180)",{"lhs":4319,"rhs":4320},"tan(45*pi\u002F180 + pi\u002F2)","-1","k \\in \\mathbb{Z};\\ \\text{beim Tangens}\\ x \\neq \\frac{\\pi}{2} + m\\pi,\\ m \\in \\mathbb{Z}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\mathbb{Z};\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003Cspan class=\"mpunct\">;\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">beim Tangens\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq \\frac{\\pi}{2} + m\\pi,\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\">x\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:1.0404em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">mπ\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>m\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m \\in \\mathbb{Z}\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4326,"x":4327,"y":4330,"unit":4333,"items":4334},"Graph von sin x über zwei Perioden von 0 bis 4π; nach 2π wiederholt sich der Verlauf",[4328,4329],-0.7,9,[4331,4332],-1.7,1.8,32,[4335,4341,4344,4351,4355,4361,4366,4370,4374,4378,4383],{"type":4336,"from":4337,"to":4339,"style":4340},"segment",[4328,4338],0,[4329,4338],"muted",{"type":4336,"from":4342,"to":4343,"style":4340},[4338,4331],[4338,4332],{"type":4336,"from":4345,"to":4348,"style":4350},[4346,4347],4,-1.5,[4346,4349],1.6,"dashed",{"type":4336,"from":4352,"to":4354,"style":4350},[4353,4347],8,[4353,4349],{"type":4356,"expr":4357,"domain":4358},"function","1.2 * sin(x * pi \u002F 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