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Bei ",[572,886,888,913],{"className":887},[579],[572,889,891],{"className":890},[583],[585,892,893],{"xmlns":587},[590,894,895,910],{},[593,896,897,899,901],{},[596,898,605],{},[600,900,608],{},[902,903,904,907],"msup",{},[800,905,906],{},"90",[600,908,909],{},"∘",[631,911,912],{"encoding":633},"\\alpha = 90^\\circ",[572,914,916,935],{"className":915,"ariaHidden":639},[638],[572,917,919,923,926,929,932],{"className":918},[643],[572,920],{"className":921,"style":922},[647],"height:0.4306em;",[572,924,605],{"className":925,"style":663},[661,662],[572,927],{"className":928,"style":667},[656],[572,930,608],{"className":931},[671],[572,933],{"className":934,"style":667},[656],[572,936,938,942,946],{"className":937},[643],[572,939],{"className":940,"style":941},[647],"height:0.6741em;",[572,943,945],{"className":944},[661],"9",[572,947,949,952],{"className":948},[661],[572,950,802],{"className":951},[661],[572,953,956],{"className":954},[955],"msupsub",[572,957,959],{"className":958},[696],[572,960,962],{"className":961},[701],[572,963,965],{"className":964,"style":941},[705],[572,966,968,972],{"style":967},"top:-3.063em;margin-right:0.05em;",[572,969],{"className":970,"style":971},[713],"height:2.7em;",[572,973,979],{"className":974},[975,976,977,978],"sizing","reset-size6","size3","mtight",[572,980,909],{"className":981},[982,978],"mbin",", ",[572,985,987,1006],{"className":986},[579],[572,988,990],{"className":989},[583],[585,991,992],{"xmlns":587},[590,993,994,1003],{},[593,995,996],{},[902,997,998,1001],{},[800,999,1000],{},"270",[600,1002,909],{},[631,1004,1005],{"encoding":633},"270^\\circ",[572,1007,1009],{"className":1008,"ariaHidden":639},[638],[572,1010,1012,1015,1019],{"className":1011},[643],[572,1013],{"className":1014,"style":941},[647],[572,1016,1018],{"className":1017},[661],"27",[572,1020,1022,1025],{"className":1021},[661],[572,1023,802],{"className":1024},[661],[572,1026,1028],{"className":1027},[955],[572,1029,1031],{"className":1030},[696],[572,1032,1034],{"className":1033},[701],[572,1035,1037],{"className":1036,"style":941},[705],[572,1038,1039,1042],{"style":967},[572,1040],{"className":1041,"style":971},[713],[572,1043,1045],{"className":1044},[975,976,977,978],[572,1046,909],{"className":1047},[982,978]," usw. ist der Kosinus null, und der Tangens ist dort ",[567,1050,1051],{},"nicht definiert",".",[563,1054,1055,1056,1201],{},"Im rechtwinkligen Dreieck passt die Formel zur Definition ",[572,1057,1059,1088],{"className":1058},[579],[572,1060,1062],{"className":1061},[583],[585,1063,1064],{"xmlns":587},[590,1065,1066,1085],{},[593,1067,1068,1070,1072,1074,1076],{},[596,1069,598],{},[600,1071,602],{},[596,1073,605],{},[600,1075,608],{},[610,1077,1078,1082],{},[1079,1080,1081],"mtext",{},"Gegenkathete",[1079,1083,1084],{},"Ankathete",[631,1086,1087],{"encoding":633},"\\tan \\alpha = \\frac{\\text{Gegenkathete}}{\\text{Ankathete}}",[572,1089,1091,1115],{"className":1090,"ariaHidden":639},[638],[572,1092,1094,1097,1100,1103,1106,1109,1112],{"className":1093},[643],[572,1095],{"className":1096,"style":648},[647],[572,1098,598],{"className":1099},[652],[572,1101],{"className":1102,"style":657},[656],[572,1104,605],{"className":1105,"style":663},[661,662],[572,1107],{"className":1108,"style":667},[656],[572,1110,608],{"className":1111},[671],[572,1113],{"className":1114,"style":667},[656],[572,1116,1118,1122],{"className":1117},[643],[572,1119],{"className":1120,"style":1121},[647],"height:1.2772em;vertical-align:-0.345em;",[572,1123,1125,1128,1198],{"className":1124},[661],[572,1126],{"className":1127},[688,689],[572,1129,1131],{"className":1130},[610],[572,1132,1134,1189],{"className":1133},[696,697],[572,1135,1137,1186],{"className":1136},[701],[572,1138,1141,1160,1168],{"className":1139,"style":1140},[705],"height:0.9322em;",[572,1142,1144,1147],{"style":1143},"top:-2.655em;",[572,1145],{"className":1146,"style":714},[713],[572,1148,1150],{"className":1149},[975,976,977,978],[572,1151,1153],{"className":1152},[661,978],[572,1154,1157],{"className":1155},[661,1156,978],"text",[572,1158,1084],{"className":1159},[661,978],[572,1161,1162,1165],{"style":729},[572,1163],{"className":1164,"style":714},[713],[572,1166],{"className":1167,"style":737},[736],[572,1169,1171,1174],{"style":1170},"top:-3.4461em;",[572,1172],{"className":1173,"style":714},[713],[572,1175,1177],{"className":1176},[975,976,977,978],[572,1178,1180],{"className":1179},[661,978],[572,1181,1183],{"className":1182},[661,1156,978],[572,1184,1081],{"className":1185},[661,978],[572,1187,760],{"className":1188},[759],[572,1190,1192],{"className":1191},[701],[572,1193,1196],{"className":1194,"style":1195},[705],"height:0.345em;",[572,1197],{},[572,1199],{"className":1200},[773,689],". Für beliebige Winkel (ab Klasse 10) werden Sinus und Kosinus am Einheitskreis definiert; dann dient die Formel als Definition des Tangens.",[558,1203,1205],{"id":1204},"herleitung","Herleitung",[563,1207,1208,1209,1345,1346,1479,1480,1508],{},"Im rechtwinkligen Dreieck ist ",[572,1210,1212,1240],{"className":1211},[579],[572,1213,1215],{"className":1214},[583],[585,1216,1217],{"xmlns":587},[590,1218,1219,1237],{},[593,1220,1221,1223,1225,1227,1229],{},[596,1222,616],{},[600,1224,602],{},[596,1226,605],{},[600,1228,608],{},[610,1230,1231,1234],{},[596,1232,1233],{},"a",[596,1235,1236],{},"c",[631,1238,1239],{"encoding":633},"\\sin \\alpha = \\frac{a}{c}",[572,1241,1243,1268],{"className":1242,"ariaHidden":639},[638],[572,1244,1246,1250,1253,1256,1259,1262,1265],{"className":1245},[643],[572,1247],{"className":1248,"style":1249},[647],"height:0.6679em;",[572,1251,616],{"className":1252},[652],[572,1254],{"className":1255,"style":657},[656],[572,1257,605],{"className":1258,"style":663},[661,662],[572,1260],{"className":1261,"style":667},[656],[572,1263,608],{"className":1264},[671],[572,1266],{"className":1267,"style":667},[656],[572,1269,1271,1275],{"className":1270},[643],[572,1272],{"className":1273,"style":1274},[647],"height:1.0404em;vertical-align:-0.345em;",[572,1276,1278,1281,1342],{"className":1277},[661],[572,1279],{"className":1280},[688,689],[572,1282,1284],{"className":1283},[610],[572,1285,1287,1334],{"className":1286},[696,697],[572,1288,1290,1331],{"className":1289},[701],[572,1291,1294,1308,1316],{"className":1292,"style":1293},[705],"height:0.6954em;",[572,1295,1296,1299],{"style":1143},[572,1297],{"className":1298,"style":714},[713],[572,1300,1302],{"className":1301},[975,976,977,978],[572,1303,1305],{"className":1304},[661,978],[572,1306,1236],{"className":1307},[661,662,978],[572,1309,1310,1313],{"style":729},[572,1311],{"className":1312,"style":714},[713],[572,1314],{"className":1315,"style":737},[736],[572,1317,1319,1322],{"style":1318},"top:-3.394em;",[572,1320],{"className":1321,"style":714},[713],[572,1323,1325],{"className":1324},[975,976,977,978],[572,1326,1328],{"className":1327},[661,978],[572,1329,1233],{"className":1330},[661,662,978],[572,1332,760],{"className":1333},[759],[572,1335,1337],{"className":1336},[701],[572,1338,1340],{"className":1339,"style":1195},[705],[572,1341],{},[572,1343],{"className":1344},[773,689]," und ",[572,1347,1349,1376],{"className":1348},[579],[572,1350,1352],{"className":1351},[583],[585,1353,1354],{"xmlns":587},[590,1355,1356,1373],{},[593,1357,1358,1360,1362,1364,1366],{},[596,1359,625],{},[600,1361,602],{},[596,1363,605],{},[600,1365,608],{},[610,1367,1368,1371],{},[596,1369,1370],{},"b",[596,1372,1236],{},[631,1374,1375],{"encoding":633},"\\cos \\alpha = \\frac{b}{c}",[572,1377,1379,1403],{"className":1378,"ariaHidden":639},[638],[572,1380,1382,1385,1388,1391,1394,1397,1400],{"className":1381},[643],[572,1383],{"className":1384,"style":922},[647],[572,1386,625],{"className":1387},[652],[572,1389],{"className":1390,"style":657},[656],[572,1392,605],{"className":1393,"style":663},[661,662],[572,1395],{"className":1396,"style":667},[656],[572,1398,608],{"className":1399},[671],[572,1401],{"className":1402,"style":667},[656],[572,1404,1406,1410],{"className":1405},[643],[572,1407],{"className":1408,"style":1409},[647],"height:1.2251em;vertical-align:-0.345em;",[572,1411,1413,1416,1476],{"className":1412},[661],[572,1414],{"className":1415},[688,689],[572,1417,1419],{"className":1418},[610],[572,1420,1422,1468],{"className":1421},[696,697],[572,1423,1425,1465],{"className":1424},[701],[572,1426,1429,1443,1451],{"className":1427,"style":1428},[705],"height:0.8801em;",[572,1430,1431,1434],{"style":1143},[572,1432],{"className":1433,"style":714},[713],[572,1435,1437],{"className":1436},[975,976,977,978],[572,1438,1440],{"className":1439},[661,978],[572,1441,1236],{"className":1442},[661,662,978],[572,1444,1445,1448],{"style":729},[572,1446],{"className":1447,"style":714},[713],[572,1449],{"className":1450,"style":737},[736],[572,1452,1453,1456],{"style":1318},[572,1454],{"className":1455,"style":714},[713],[572,1457,1459],{"className":1458},[975,976,977,978],[572,1460,1462],{"className":1461},[661,978],[572,1463,1370],{"className":1464},[661,662,978],[572,1466,760],{"className":1467},[759],[572,1469,1471],{"className":1470},[701],[572,1472,1474],{"className":1473,"style":1195},[705],[572,1475],{},[572,1477],{"className":1478},[773,689],". Beim Teilen kürzt sich die Hypotenuse ",[572,1481,1483,1496],{"className":1482},[579],[572,1484,1486],{"className":1485},[583],[585,1487,1488],{"xmlns":587},[590,1489,1490,1494],{},[593,1491,1492],{},[596,1493,1236],{},[631,1495,1236],{"encoding":633},[572,1497,1499],{"className":1498,"ariaHidden":639},[638],[572,1500,1502,1505],{"className":1501},[643],[572,1503],{"className":1504,"style":922},[647],[572,1506,1236],{"className":1507},[661,662]," heraus:",[572,1510,1512],{"className":1511},[575],[572,1513,1515,1595],{"className":1514},[579],[572,1516,1518],{"className":1517},[583],[585,1519,1520],{"xmlns":587,"display":588},[590,1521,1522,1592],{},[593,1523,1524,1542,1544,1550,1553,1559,1561,1567,1570,1576,1578,1584,1586,1588,1590],{},[610,1525,1526,1534],{},[593,1527,1528,1530,1532],{},[596,1529,616],{},[600,1531,602],{},[596,1533,605],{},[593,1535,1536,1538,1540],{},[596,1537,625],{},[600,1539,602],{},[596,1541,605],{},[600,1543,608],{},[610,1545,1546,1548],{},[596,1547,1233],{},[596,1549,1236],{},[600,1551,1552],{},":",[610,1554,1555,1557],{},[596,1556,1370],{},[596,1558,1236],{},[600,1560,608],{},[610,1562,1563,1565],{},[596,1564,1233],{},[596,1566,1236],{},[600,1568,1569],{},"⋅",[610,1571,1572,1574],{},[596,1573,1236],{},[596,1575,1370],{},[600,1577,608],{},[610,1579,1580,1582],{},[596,1581,1233],{},[596,1583,1370],{},[600,1585,608],{},[596,1587,598],{},[600,1589,602],{},[596,1591,605],{},[631,1593,1594],{"encoding":633},"\\frac{\\sin \\alpha}{\\cos \\alpha} = \\frac{a}{c} : \\frac{b}{c} = \\frac{a}{c} \\cdot \\frac{c}{b} = \\frac{a}{b} = \\tan \\alpha",[572,1596,1598,1687,1766,1845,1923,2000,2077],{"className":1597,"ariaHidden":639},[638],[572,1599,1601,1604,1678,1681,1684],{"className":1600},[643],[572,1602],{"className":1603,"style":681},[647],[572,1605,1607,1610,1675],{"className":1606},[661],[572,1608],{"className":1609},[688,689],[572,1611,1613],{"className":1612},[610],[572,1614,1616,1667],{"className":1615},[696,697],[572,1617,1619,1664],{"className":1618},[701],[572,1620,1622,1639,1647],{"className":1621,"style":706},[705],[572,1623,1624,1627],{"style":709},[572,1625],{"className":1626,"style":714},[713],[572,1628,1630,1633,1636],{"className":1629},[661],[572,1631,625],{"className":1632},[652],[572,1634],{"className":1635,"style":657},[656],[572,1637,605],{"className":1638,"style":663},[661,662],[572,1640,1641,1644],{"style":729},[572,1642],{"className":1643,"style":714},[713],[572,1645],{"className":1646,"style":737},[736],[572,1648,1649,1652],{"style":740},[572,1650],{"className":1651,"style":714},[713],[572,1653,1655,1658,1661],{"className":1654},[661],[572,1656,616],{"className":1657},[652],[572,1659],{"className":1660,"style":657},[656],[572,1662,605],{"className":1663,"style":663},[661,662],[572,1665,760],{"className":1666},[759],[572,1668,1670],{"className":1669},[701],[572,1671,1673],{"className":1672,"style":767},[705],[572,1674],{},[572,1676],{"className":1677},[773,689],[572,1679],{"className":1680,"style":667},[656],[572,1682,608],{"className":1683},[671],[572,1685],{"className":1686,"style":667},[656],[572,1688,1690,1694,1757,1760,1763],{"className":1689},[643],[572,1691],{"className":1692,"style":1693},[647],"height:1.7936em;vertical-align:-0.686em;",[572,1695,1697,1700,1754],{"className":1696},[661],[572,1698],{"className":1699},[688,689],[572,1701,1703],{"className":1702},[610],[572,1704,1706,1746],{"className":1705},[696,697],[572,1707,1709,1743],{"className":1708},[701],[572,1710,1713,1724,1732],{"className":1711,"style":1712},[705],"height:1.1076em;",[572,1714,1715,1718],{"style":709},[572,1716],{"className":1717,"style":714},[713],[572,1719,1721],{"className":1720},[661],[572,1722,1236],{"className":1723},[661,662],[572,1725,1726,1729],{"style":729},[572,1727],{"className":1728,"style":714},[713],[572,1730],{"className":1731,"style":737},[736],[572,1733,1734,1737],{"style":740},[572,1735],{"className":1736,"style":714},[713],[572,1738,1740],{"className":1739},[661],[572,1741,1233],{"className":1742},[661,662],[572,1744,760],{"className":1745},[759],[572,1747,1749],{"className":1748},[701],[572,1750,1752],{"className":1751,"style":767},[705],[572,1753],{},[572,1755],{"className":1756},[773,689],[572,1758],{"className":1759,"style":667},[656],[572,1761,1552],{"className":1762},[671],[572,1764],{"className":1765,"style":667},[656],[572,1767,1769,1773,1836,1839,1842],{"className":1768},[643],[572,1770],{"className":1771,"style":1772},[647],"height:2.0574em;vertical-align:-0.686em;",[572,1774,1776,1779,1833],{"className":1775},[661],[572,1777],{"className":1778},[688,689],[572,1780,1782],{"className":1781},[610],[572,1783,1785,1825],{"className":1784},[696,697],[572,1786,1788,1822],{"className":1787},[701],[572,1789,1792,1803,1811],{"className":1790,"style":1791},[705],"height:1.3714em;",[572,1793,1794,1797],{"style":709},[572,1795],{"className":1796,"style":714},[713],[572,1798,1800],{"className":1799},[661],[572,1801,1236],{"className":1802},[661,662],[572,1804,1805,1808],{"style":729},[572,1806],{"className":1807,"style":714},[713],[572,1809],{"className":1810,"style":737},[736],[572,1812,1813,1816],{"style":740},[572,1814],{"className":1815,"style":714},[713],[572,1817,1819],{"className":1818},[661],[572,1820,1370],{"className":1821},[661,662],[572,1823,760],{"className":1824},[759],[572,1826,1828],{"className":1827},[701],[572,1829,1831],{"className":1830,"style":767},[705],[572,1832],{},[572,1834],{"className":1835},[773,689],[572,1837],{"className":1838,"style":667},[656],[572,1840,608],{"className":1841},[671],[572,1843],{"className":1844,"style":667},[656],[572,1846,1848,1851,1913,1917,1920],{"className":1847},[643],[572,1849],{"className":1850,"style":1693},[647],[572,1852,1854,1857,1910],{"className":1853},[661],[572,1855],{"className":1856},[688,689],[572,1858,1860],{"className":1859},[610],[572,1861,1863,1902],{"className":1862},[696,697],[572,1864,1866,1899],{"className":1865},[701],[572,1867,1869,1880,1888],{"className":1868,"style":1712},[705],[572,1870,1871,1874],{"style":709},[572,1872],{"className":1873,"style":714},[713],[572,1875,1877],{"className":1876},[661],[572,1878,1236],{"className":1879},[661,662],[572,1881,1882,1885],{"style":729},[572,1883],{"className":1884,"style":714},[713],[572,1886],{"className":1887,"style":737},[736],[572,1889,1890,1893],{"style":740},[572,1891],{"className":1892,"style":714},[713],[572,1894,1896],{"className":1895},[661],[572,1897,1233],{"className":1898},[661,662],[572,1900,760],{"className":1901},[759],[572,1903,1905],{"className":1904},[701],[572,1906,1908],{"className":1907,"style":767},[705],[572,1909],{},[572,1911],{"className":1912},[773,689],[572,1914],{"className":1915,"style":1916},[656],"margin-right:0.2222em;",[572,1918,1569],{"className":1919},[982],[572,1921],{"className":1922,"style":1916},[656],[572,1924,1926,1929,1991,1994,1997],{"className":1925},[643],[572,1927],{"className":1928,"style":1693},[647],[572,1930,1932,1935,1988],{"className":1931},[661],[572,1933],{"className":1934},[688,689],[572,1936,1938],{"className":1937},[610],[572,1939,1941,1980],{"className":1940},[696,697],[572,1942,1944,1977],{"className":1943},[701],[572,1945,1947,1958,1966],{"className":1946,"style":1712},[705],[572,1948,1949,1952],{"style":709},[572,1950],{"className":1951,"style":714},[713],[572,1953,1955],{"className":1954},[661],[572,1956,1370],{"className":1957},[661,662],[572,1959,1960,1963],{"style":729},[572,1961],{"className":1962,"style":714},[713],[572,1964],{"className":1965,"style":737},[736],[572,1967,1968,1971],{"style":740},[572,1969],{"className":1970,"style":714},[713],[572,1972,1974],{"className":1973},[661],[572,1975,1236],{"className":1976},[661,662],[572,1978,760],{"className":1979},[759],[572,1981,1983],{"className":1982},[701],[572,1984,1986],{"className":1985,"style":767},[705],[572,1987],{},[572,1989],{"className":1990},[773,689],[572,1992],{"className":1993,"style":667},[656],[572,1995,608],{"className":1996},[671],[572,1998],{"className":1999,"style":667},[656],[572,2001,2003,2006,2068,2071,2074],{"className":2002},[643],[572,2004],{"className":2005,"style":1693},[647],[572,2007,2009,2012,2065],{"className":2008},[661],[572,2010],{"className":2011},[688,689],[572,2013,2015],{"className":2014},[610],[572,2016,2018,2057],{"className":2017},[696,697],[572,2019,2021,2054],{"className":2020},[701],[572,2022,2024,2035,2043],{"className":2023,"style":1712},[705],[572,2025,2026,2029],{"style":709},[572,2027],{"className":2028,"style":714},[713],[572,2030,2032],{"className":2031},[661],[572,2033,1370],{"className":2034},[661,662],[572,2036,2037,2040],{"style":729},[572,2038],{"className":2039,"style":714},[713],[572,2041],{"className":2042,"style":737},[736],[572,2044,2045,2048],{"style":740},[572,2046],{"className":2047,"style":714},[713],[572,2049,2051],{"className":2050},[661],[572,2052,1233],{"className":2053},[661,662],[572,2055,760],{"className":2056},[759],[572,2058,2060],{"className":2059},[701],[572,2061,2063],{"className":2062,"style":767},[705],[572,2064],{},[572,2066],{"className":2067},[773,689],[572,2069],{"className":2070,"style":667},[656],[572,2072,608],{"className":2073},[671],[572,2075],{"className":2076,"style":667},[656],[572,2078,2080,2083,2086,2089],{"className":2079},[643],[572,2081],{"className":2082,"style":648},[647],[572,2084,598],{"className":2085},[652],[572,2087],{"className":2088,"style":657},[656],[572,2090,605],{"className":2091,"style":663},[661,662],[558,2093,2095],{"id":2094},"beispiele","Beispiele",[563,2097,2098,2099,1345,2174,1552],{},"Für einen Winkel gilt ",[572,2100,2102,2125],{"className":2101},[579],[572,2103,2105],{"className":2104},[583],[585,2106,2107],{"xmlns":587},[590,2108,2109,2122],{},[593,2110,2111,2113,2115,2117,2119],{},[596,2112,616],{},[600,2114,602],{},[596,2116,605],{},[600,2118,608],{},[800,2120,2121],{},"0,6",[631,2123,2124],{"encoding":633},"\\sin \\alpha = 0{,}6",[572,2126,2128,2152],{"className":2127,"ariaHidden":639},[638],[572,2129,2131,2134,2137,2140,2143,2146,2149],{"className":2130},[643],[572,2132],{"className":2133,"style":1249},[647],[572,2135,616],{"className":2136},[652],[572,2138],{"className":2139,"style":657},[656],[572,2141,605],{"className":2142,"style":663},[661,662],[572,2144],{"className":2145,"style":667},[656],[572,2147,608],{"className":2148},[671],[572,2150],{"className":2151,"style":667},[656],[572,2153,2155,2159,2162,2170],{"className":2154},[643],[572,2156],{"className":2157,"style":2158},[647],"height:0.8389em;vertical-align:-0.1944em;",[572,2160,802],{"className":2161},[661],[572,2163,2165],{"className":2164},[661],[572,2166,2169],{"className":2167},[2168],"mpunct",",",[572,2171,2173],{"className":2172},[661],"6",[572,2175,2177,2200],{"className":2176},[579],[572,2178,2180],{"className":2179},[583],[585,2181,2182],{"xmlns":587},[590,2183,2184,2197],{},[593,2185,2186,2188,2190,2192,2194],{},[596,2187,625],{},[600,2189,602],{},[596,2191,605],{},[600,2193,608],{},[800,2195,2196],{},"0,8",[631,2198,2199],{"encoding":633},"\\cos \\alpha = 0{,}8",[572,2201,2203,2227],{"className":2202,"ariaHidden":639},[638],[572,2204,2206,2209,2212,2215,2218,2221,2224],{"className":2205},[643],[572,2207],{"className":2208,"style":922},[647],[572,2210,625],{"className":2211},[652],[572,2213],{"className":2214,"style":657},[656],[572,2216,605],{"className":2217,"style":663},[661,662],[572,2219],{"className":2220,"style":667},[656],[572,2222,608],{"className":2223},[671],[572,2225],{"className":2226,"style":667},[656],[572,2228,2230,2233,2236,2242],{"className":2229},[643],[572,2231],{"className":2232,"style":2158},[647],[572,2234,802],{"className":2235},[661],[572,2237,2239],{"className":2238},[661],[572,2240,2169],{"className":2241},[2168],[572,2243,2245],{"className":2244},[661],"8",[572,2247,2249],{"className":2248},[575],[572,2250,2252,2283],{"className":2251},[579],[572,2253,2255],{"className":2254},[583],[585,2256,2257],{"xmlns":587,"display":588},[590,2258,2259,2280],{},[593,2260,2261,2263,2265,2267,2269,2275,2277],{},[596,2262,598],{},[600,2264,602],{},[596,2266,605],{},[600,2268,608],{},[610,2270,2271,2273],{},[800,2272,2121],{},[800,2274,2196],{},[600,2276,608],{},[800,2278,2279],{},"0,75",[631,2281,2282],{"encoding":633},"\\tan \\alpha = \\frac{0{,}6}{0{,}8} = 0{,}75",[572,2284,2286,2310,2408],{"className":2285,"ariaHidden":639},[638],[572,2287,2289,2292,2295,2298,2301,2304,2307],{"className":2288},[643],[572,2290],{"className":2291,"style":648},[647],[572,2293,598],{"className":2294},[652],[572,2296],{"className":2297,"style":657},[656],[572,2299,605],{"className":2300,"style":663},[661,662],[572,2302],{"className":2303,"style":667},[656],[572,2305,608],{"className":2306},[671],[572,2308],{"className":2309,"style":667},[656],[572,2311,2313,2317,2399,2402,2405],{"className":2312},[643],[572,2314],{"className":2315,"style":2316},[647],"height:2.2019em;vertical-align:-0.8804em;",[572,2318,2320,2323,2396],{"className":2319},[661],[572,2321],{"className":2322},[688,689],[572,2324,2326],{"className":2325},[610],[572,2327,2329,2387],{"className":2328},[696,697],[572,2330,2332,2384],{"className":2331},[701],[572,2333,2336,2356,2364],{"className":2334,"style":2335},[705],"height:1.3214em;",[572,2337,2338,2341],{"style":709},[572,2339],{"className":2340,"style":714},[713],[572,2342,2344,2347,2353],{"className":2343},[661],[572,2345,802],{"className":2346},[661],[572,2348,2350],{"className":2349},[661],[572,2351,2169],{"className":2352},[2168],[572,2354,2245],{"className":2355},[661],[572,2357,2358,2361],{"style":729},[572,2359],{"className":2360,"style":714},[713],[572,2362],{"className":2363,"style":737},[736],[572,2365,2366,2369],{"style":740},[572,2367],{"className":2368,"style":714},[713],[572,2370,2372,2375,2381],{"className":2371},[661],[572,2373,802],{"className":2374},[661],[572,2376,2378],{"className":2377},[661],[572,2379,2169],{"className":2380},[2168],[572,2382,2173],{"className":2383},[661],[572,2385,760],{"className":2386},[759],[572,2388,2390],{"className":2389},[701],[572,2391,2394],{"className":2392,"style":2393},[705],"height:0.8804em;",[572,2395],{},[572,2397],{"className":2398},[773,689],[572,2400],{"className":2401,"style":667},[656],[572,2403,608],{"className":2404},[671],[572,2406],{"className":2407,"style":667},[656],[572,2409,2411,2414,2417,2423],{"className":2410},[643],[572,2412],{"className":2413,"style":2158},[647],[572,2415,802],{"className":2416},[661],[572,2418,2420],{"className":2419},[661],[572,2421,2169],{"className":2422},[2168],[572,2424,2426],{"className":2425},[661],"75",[563,2428,2429,2430,2495],{},"Bei ",[572,2431,2433,2452],{"className":2432},[579],[572,2434,2436],{"className":2435},[583],[585,2437,2438],{"xmlns":587},[590,2439,2440,2449],{},[593,2441,2442],{},[902,2443,2444,2447],{},[800,2445,2446],{},"45",[600,2448,909],{},[631,2450,2451],{"encoding":633},"45^\\circ",[572,2453,2455],{"className":2454,"ariaHidden":639},[638],[572,2456,2458,2461,2465],{"className":2457},[643],[572,2459],{"className":2460,"style":941},[647],[572,2462,2464],{"className":2463},[661],"4",[572,2466,2468,2472],{"className":2467},[661],[572,2469,2471],{"className":2470},[661],"5",[572,2473,2475],{"className":2474},[955],[572,2476,2478],{"className":2477},[696],[572,2479,2481],{"className":2480},[701],[572,2482,2484],{"className":2483,"style":941},[705],[572,2485,2486,2489],{"style":967},[572,2487],{"className":2488,"style":971},[713],[572,2490,2492],{"className":2491},[975,976,977,978],[572,2493,909],{"className":2494},[982,978]," sind Sinus und Kosinus gleich, also:",[572,2497,2499],{"className":2498},[575],[572,2500,2502,2557],{"className":2501},[579],[572,2503,2505],{"className":2504},[583],[585,2506,2507],{"xmlns":587,"display":588},[590,2508,2509,2554],{},[593,2510,2511,2513,2515,2521,2523,2549,2551],{},[596,2512,598],{},[600,2514,602],{},[902,2516,2517,2519],{},[800,2518,2446],{},[600,2520,909],{},[600,2522,608],{},[610,2524,2525,2537],{},[593,2526,2527,2529,2531],{},[596,2528,616],{},[600,2530,602],{},[902,2532,2533,2535],{},[800,2534,2446],{},[600,2536,909],{},[593,2538,2539,2541,2543],{},[596,2540,625],{},[600,2542,602],{},[902,2544,2545,2547],{},[800,2546,2446],{},[600,2548,909],{},[600,2550,608],{},[800,2552,2553],{},"1",[631,2555,2556],{"encoding":633},"\\tan 45^\\circ = \\frac{\\sin 45^\\circ}{\\cos 45^\\circ} = 1",[572,2558,2560,2615,2766],{"className":2559,"ariaHidden":639},[638],[572,2561,2563,2567,2570,2573,2576,2606,2609,2612],{"className":2562},[643],[572,2564],{"className":2565,"style":2566},[647],"height:0.7241em;",[572,2568,598],{"className":2569},[652],[572,2571],{"className":2572,"style":657},[656],[572,2574,2464],{"className":2575},[661],[572,2577,2579,2582],{"className":2578},[661],[572,2580,2471],{"className":2581},[661],[572,2583,2585],{"className":2584},[955],[572,2586,2588],{"className":2587},[696],[572,2589,2591],{"className":2590},[701],[572,2592,2594],{"className":2593,"style":2566},[705],[572,2595,2597,2600],{"style":2596},"top:-3.113em;margin-right:0.05em;",[572,2598],{"className":2599,"style":971},[713],[572,2601,2603],{"className":2602},[975,976,977,978],[572,2604,909],{"className":2605},[982,978],[572,2607],{"className":2608,"style":667},[656],[572,2610,608],{"className":2611},[671],[572,2613],{"className":2614,"style":667},[656],[572,2616,2618,2622,2757,2760,2763],{"className":2617},[643],[572,2619],{"className":2620,"style":2621},[647],"height:2.0371em;vertical-align:-0.686em;",[572,2623,2625,2628,2754],{"className":2624},[661],[572,2626],{"className":2627},[688,689],[572,2629,2631],{"className":2630},[610],[572,2632,2634,2746],{"className":2633},[696,697],[572,2635,2637,2743],{"className":2636},[701],[572,2638,2641,2689,2697],{"className":2639,"style":2640},[705],"height:1.3511em;",[572,2642,2643,2646],{"style":709},[572,2644],{"className":2645,"style":714},[713],[572,2647,2649,2652,2655,2658],{"className":2648},[661],[572,2650,625],{"className":2651},[652],[572,2653],{"className":2654,"style":657},[656],[572,2656,2464],{"className":2657},[661],[572,2659,2661,2664],{"className":2660},[661],[572,2662,2471],{"className":2663},[661],[572,2665,2667],{"className":2666},[955],[572,2668,2670],{"className":2669},[696],[572,2671,2673],{"className":2672},[701],[572,2674,2677],{"className":2675,"style":2676},[705],"height:0.6001em;",[572,2678,2680,2683],{"style":2679},"top:-2.989em;margin-right:0.05em;",[572,2681],{"className":2682,"style":971},[713],[572,2684,2686],{"className":2685},[975,976,977,978],[572,2687,909],{"className":2688},[982,978],[572,2690,2691,2694],{"style":729},[572,2692],{"className":2693,"style":714},[713],[572,2695],{"className":2696,"style":737},[736],[572,2698,2699,2702],{"style":740},[572,2700],{"className":2701,"style":714},[713],[572,2703,2705,2708,2711,2714],{"className":2704},[661],[572,2706,616],{"className":2707},[652],[572,2709],{"className":2710,"style":657},[656],[572,2712,2464],{"className":2713},[661],[572,2715,2717,2720],{"className":2716},[661],[572,2718,2471],{"className":2719},[661],[572,2721,2723],{"className":2722},[955],[572,2724,2726],{"className":2725},[696],[572,2727,2729],{"className":2728},[701],[572,2730,2732],{"className":2731,"style":941},[705],[572,2733,2734,2737],{"style":967},[572,2735],{"className":2736,"style":971},[713],[572,2738,2740],{"className":2739},[975,976,977,978],[572,2741,909],{"className":2742},[982,978],[572,2744,760],{"className":2745},[759],[572,2747,2749],{"className":2748},[701],[572,2750,2752],{"className":2751,"style":767},[705],[572,2753],{},[572,2755],{"className":2756},[773,689],[572,2758],{"className":2759,"style":667},[656],[572,2761,608],{"className":2762},[671],[572,2764],{"className":2765,"style":667},[656],[572,2767,2769,2772],{"className":2768},[643],[572,2770],{"className":2771,"style":880},[647],[572,2773,2553],{"className":2774},[661],[563,2776,2777,2778,2861,2862,2956,2957,3019],{},"Für ",[572,2779,2781,2802],{"className":2780},[579],[572,2782,2784],{"className":2783},[583],[585,2785,2786],{"xmlns":587},[590,2787,2788,2800],{},[593,2789,2790,2792,2794],{},[596,2791,605],{},[600,2793,608],{},[902,2795,2796,2798],{},[800,2797,906],{},[600,2799,909],{},[631,2801,912],{"encoding":633},[572,2803,2805,2823],{"className":2804,"ariaHidden":639},[638],[572,2806,2808,2811,2814,2817,2820],{"className":2807},[643],[572,2809],{"className":2810,"style":922},[647],[572,2812,605],{"className":2813,"style":663},[661,662],[572,2815],{"className":2816,"style":667},[656],[572,2818,608],{"className":2819},[671],[572,2821],{"className":2822,"style":667},[656],[572,2824,2826,2829,2832],{"className":2825},[643],[572,2827],{"className":2828,"style":941},[647],[572,2830,945],{"className":2831},[661],[572,2833,2835,2838],{"className":2834},[661],[572,2836,802],{"className":2837},[661],[572,2839,2841],{"className":2840},[955],[572,2842,2844],{"className":2843},[696],[572,2845,2847],{"className":2846},[701],[572,2848,2850],{"className":2849,"style":941},[705],[572,2851,2852,2855],{"style":967},[572,2853],{"className":2854,"style":971},[713],[572,2856,2858],{"className":2857},[975,976,977,978],[572,2859,909],{"className":2860},[982,978]," ist ",[572,2863,2865,2891],{"className":2864},[579],[572,2866,2868],{"className":2867},[583],[585,2869,2870],{"xmlns":587},[590,2871,2872,2888],{},[593,2873,2874,2876,2878,2884,2886],{},[596,2875,625],{},[600,2877,602],{},[902,2879,2880,2882],{},[800,2881,906],{},[600,2883,909],{},[600,2885,608],{},[800,2887,802],{},[631,2889,2890],{"encoding":633},"\\cos 90^\\circ = 0",[572,2892,2894,2947],{"className":2893,"ariaHidden":639},[638],[572,2895,2897,2900,2903,2906,2909,2938,2941,2944],{"className":2896},[643],[572,2898],{"className":2899,"style":941},[647],[572,2901,625],{"className":2902},[652],[572,2904],{"className":2905,"style":657},[656],[572,2907,945],{"className":2908},[661],[572,2910,2912,2915],{"className":2911},[661],[572,2913,802],{"className":2914},[661],[572,2916,2918],{"className":2917},[955],[572,2919,2921],{"className":2920},[696],[572,2922,2924],{"className":2923},[701],[572,2925,2927],{"className":2926,"style":941},[705],[572,2928,2929,2932],{"style":967},[572,2930],{"className":2931,"style":971},[713],[572,2933,2935],{"className":2934},[975,976,977,978],[572,2936,909],{"className":2937},[982,978],[572,2939],{"className":2940,"style":667},[656],[572,2942,608],{"className":2943},[671],[572,2945],{"className":2946,"style":667},[656],[572,2948,2950,2953],{"className":2949},[643],[572,2951],{"className":2952,"style":880},[647],[572,2954,802],{"className":2955},[661],". Der Tangens von ",[572,2958,2960,2978],{"className":2959},[579],[572,2961,2963],{"className":2962},[583],[585,2964,2965],{"xmlns":587},[590,2966,2967,2975],{},[593,2968,2969],{},[902,2970,2971,2973],{},[800,2972,906],{},[600,2974,909],{},[631,2976,2977],{"encoding":633},"90^\\circ",[572,2979,2981],{"className":2980,"ariaHidden":639},[638],[572,2982,2984,2987,2990],{"className":2983},[643],[572,2985],{"className":2986,"style":941},[647],[572,2988,945],{"className":2989},[661],[572,2991,2993,2996],{"className":2992},[661],[572,2994,802],{"className":2995},[661],[572,2997,2999],{"className":2998},[955],[572,3000,3002],{"className":3001},[696],[572,3003,3005],{"className":3004},[701],[572,3006,3008],{"className":3007,"style":941},[705],[572,3009,3010,3013],{"style":967},[572,3011],{"className":3012,"style":971},[713],[572,3014,3016],{"className":3015},[975,976,977,978],[572,3017,909],{"className":3018},[982,978]," existiert nicht; der Taschenrechner meldet einen Fehler.",[558,3021,3023],{"id":3022},"typische-fehler","Typische Fehler",[3025,3026,3027,3177,3253],"ul",{},[3028,3029,3030,3031,3176],"li",{},"Den Bruch umdrehen: ",[572,3032,3034,3064],{"className":3033},[579],[572,3035,3037],{"className":3036},[583],[585,3038,3039],{"xmlns":587},[590,3040,3041,3061],{},[593,3042,3043],{},[610,3044,3045,3053],{},[593,3046,3047,3049,3051],{},[596,3048,625],{},[600,3050,602],{},[596,3052,605],{},[593,3054,3055,3057,3059],{},[596,3056,616],{},[600,3058,602],{},[596,3060,605],{},[631,3062,3063],{"encoding":633},"\\frac{\\cos \\alpha}{\\sin \\alpha}",[572,3065,3067],{"className":3066,"ariaHidden":639},[638],[572,3068,3070,3073],{"className":3069},[643],[572,3071],{"className":3072,"style":1274},[647],[572,3074,3076,3079,3173],{"className":3075},[661],[572,3077],{"className":3078},[688,689],[572,3080,3082],{"className":3081},[610],[572,3083,3085,3165],{"className":3084},[696,697],[572,3086,3088,3162],{"className":3087},[701],[572,3089,3091,3124,3132],{"className":3090,"style":1293},[705],[572,3092,3093,3096],{"style":1143},[572,3094],{"className":3095,"style":714},[713],[572,3097,3099],{"className":3098},[975,976,977,978],[572,3100,3102,3117,3121],{"className":3101},[661,978],[572,3103,3105,3109,3113],{"className":3104},[652,978],[572,3106,3108],{"className":3107},[978],"s",[572,3110,3112],{"className":3111},[978],"i",[572,3114,3116],{"className":3115},[978],"n",[572,3118],{"className":3119,"style":3120},[656,978],"margin-right:0.1952em;",[572,3122,605],{"className":3123,"style":663},[661,662,978],[572,3125,3126,3129],{"style":729},[572,3127],{"className":3128,"style":714},[713],[572,3130],{"className":3131,"style":737},[736],[572,3133,3134,3137],{"style":1318},[572,3135],{"className":3136,"style":714},[713],[572,3138,3140],{"className":3139},[975,976,977,978],[572,3141,3143,3156,3159],{"className":3142},[661,978],[572,3144,3146,3149,3153],{"className":3145},[652,978],[572,3147,1236],{"className":3148},[978],[572,3150,3152],{"className":3151},[978],"o",[572,3154,3108],{"className":3155},[978],[572,3157],{"className":3158,"style":3120},[656,978],[572,3160,605],{"className":3161,"style":663},[661,662,978],[572,3163,760],{"className":3164},[759],[572,3166,3168],{"className":3167},[701],[572,3169,3171],{"className":3170,"style":1195},[705],[572,3172],{},[572,3174],{"className":3175},[773,689]," ist der Kehrwert des Tangens, nicht der Tangens.",[3028,3178,3179,3180,3252],{},"Die Voraussetzung vergessen und ",[572,3181,3183,3205],{"className":3182},[579],[572,3184,3186],{"className":3185},[583],[585,3187,3188],{"xmlns":587},[590,3189,3190,3202],{},[593,3191,3192,3194,3196],{},[596,3193,598],{},[600,3195,602],{},[902,3197,3198,3200],{},[800,3199,906],{},[600,3201,909],{},[631,3203,3204],{"encoding":633},"\\tan 90^\\circ",[572,3206,3208],{"className":3207,"ariaHidden":639},[638],[572,3209,3211,3214,3217,3220,3223],{"className":3210},[643],[572,3212],{"className":3213,"style":941},[647],[572,3215,598],{"className":3216},[652],[572,3218],{"className":3219,"style":657},[656],[572,3221,945],{"className":3222},[661],[572,3224,3226,3229],{"className":3225},[661],[572,3227,802],{"className":3228},[661],[572,3230,3232],{"className":3231},[955],[572,3233,3235],{"className":3234},[696],[572,3236,3238],{"className":3237},[701],[572,3239,3241],{"className":3240,"style":941},[705],[572,3242,3243,3246],{"style":967},[572,3244],{"className":3245,"style":971},[713],[572,3247,3249],{"className":3248},[975,976,977,978],[572,3250,909],{"className":3251},[982,978]," berechnen wollen.",[3028,3254,3255,3256,3317,3318,2861,3462,3501,3502,3541,3542,3581],{},"Die Vorzeichen bei Winkeln über ",[572,3257,3259,3276],{"className":3258},[579],[572,3260,3262],{"className":3261},[583],[585,3263,3264],{"xmlns":587},[590,3265,3266,3274],{},[593,3267,3268],{},[902,3269,3270,3272],{},[800,3271,906],{},[600,3273,909],{},[631,3275,2977],{"encoding":633},[572,3277,3279],{"className":3278,"ariaHidden":639},[638],[572,3280,3282,3285,3288],{"className":3281},[643],[572,3283],{"className":3284,"style":941},[647],[572,3286,945],{"className":3287},[661],[572,3289,3291,3294],{"className":3290},[661],[572,3292,802],{"className":3293},[661],[572,3295,3297],{"className":3296},[955],[572,3298,3300],{"className":3299},[696],[572,3301,3303],{"className":3302},[701],[572,3304,3306],{"className":3305,"style":941},[705],[572,3307,3308,3311],{"style":967},[572,3309],{"className":3310,"style":971},[713],[572,3312,3314],{"className":3313},[975,976,977,978],[572,3315,909],{"className":3316},[982,978]," übersehen: Für ",[572,3319,3321,3353],{"className":3320},[579],[572,3322,3324],{"className":3323},[583],[585,3325,3326],{"xmlns":587},[590,3327,3328,3350],{},[593,3329,3330,3336,3339,3341,3343],{},[902,3331,3332,3334],{},[800,3333,906],{},[600,3335,909],{},[600,3337,3338],{},"\u003C",[596,3340,605],{},[600,3342,3338],{},[902,3344,3345,3348],{},[800,3346,3347],{},"180",[600,3349,909],{},[631,3351,3352],{"encoding":633},"90^\\circ \u003C \\alpha \u003C 180^\\circ",[572,3354,3356,3404,3423],{"className":3355,"ariaHidden":639},[638],[572,3357,3359,3363,3366,3395,3398,3401],{"className":3358},[643],[572,3360],{"className":3361,"style":3362},[647],"height:0.7132em;vertical-align:-0.0391em;",[572,3364,945],{"className":3365},[661],[572,3367,3369,3372],{"className":3368},[661],[572,3370,802],{"className":3371},[661],[572,3373,3375],{"className":3374},[955],[572,3376,3378],{"className":3377},[696],[572,3379,3381],{"className":3380},[701],[572,3382,3384],{"className":3383,"style":941},[705],[572,3385,3386,3389],{"style":967},[572,3387],{"className":3388,"style":971},[713],[572,3390,3392],{"className":3391},[975,976,977,978],[572,3393,909],{"className":3394},[982,978],[572,3396],{"className":3397,"style":667},[656],[572,3399,3338],{"className":3400},[671],[572,3402],{"className":3403,"style":667},[656],[572,3405,3407,3411,3414,3417,3420],{"className":3406},[643],[572,3408],{"className":3409,"style":3410},[647],"height:0.5782em;vertical-align:-0.0391em;",[572,3412,605],{"className":3413,"style":663},[661,662],[572,3415],{"className":3416,"style":667},[656],[572,3418,3338],{"className":3419},[671],[572,3421],{"className":3422,"style":667},[656],[572,3424,3426,3429,3433],{"className":3425},[643],[572,3427],{"className":3428,"style":941},[647],[572,3430,3432],{"className":3431},[661],"18",[572,3434,3436,3439],{"className":3435},[661],[572,3437,802],{"className":3438},[661],[572,3440,3442],{"className":3441},[955],[572,3443,3445],{"className":3444},[696],[572,3446,3448],{"className":3447},[701],[572,3449,3451],{"className":3450,"style":941},[705],[572,3452,3453,3456],{"style":967},[572,3454],{"className":3455,"style":971},[713],[572,3457,3459],{"className":3458},[975,976,977,978],[572,3460,909],{"className":3461},[982,978],[572,3463,3465,3483],{"className":3464},[579],[572,3466,3468],{"className":3467},[583],[585,3469,3470],{"xmlns":587},[590,3471,3472,3480],{},[593,3473,3474,3476,3478],{},[596,3475,616],{},[600,3477,602],{},[596,3479,605],{},[631,3481,3482],{"encoding":633},"\\sin \\alpha",[572,3484,3486],{"className":3485,"ariaHidden":639},[638],[572,3487,3489,3492,3495,3498],{"className":3488},[643],[572,3490],{"className":3491,"style":1249},[647],[572,3493,616],{"className":3494},[652],[572,3496],{"className":3497,"style":657},[656],[572,3499,605],{"className":3500,"style":663},[661,662]," positiv, ",[572,3503,3505,3523],{"className":3504},[579],[572,3506,3508],{"className":3507},[583],[585,3509,3510],{"xmlns":587},[590,3511,3512,3520],{},[593,3513,3514,3516,3518],{},[596,3515,625],{},[600,3517,602],{},[596,3519,605],{},[631,3521,3522],{"encoding":633},"\\cos \\alpha",[572,3524,3526],{"className":3525,"ariaHidden":639},[638],[572,3527,3529,3532,3535,3538],{"className":3528},[643],[572,3530],{"className":3531,"style":922},[647],[572,3533,625],{"className":3534},[652],[572,3536],{"className":3537,"style":657},[656],[572,3539,605],{"className":3540,"style":663},[661,662]," aber negativ, also ist ",[572,3543,3545,3563],{"className":3544},[579],[572,3546,3548],{"className":3547},[583],[585,3549,3550],{"xmlns":587},[590,3551,3552,3560],{},[593,3553,3554,3556,3558],{},[596,3555,598],{},[600,3557,602],{},[596,3559,605],{},[631,3561,3562],{"encoding":633},"\\tan \\alpha",[572,3564,3566],{"className":3565,"ariaHidden":639},[638],[572,3567,3569,3572,3575,3578],{"className":3568},[643],[572,3570],{"className":3571,"style":648},[647],[572,3573,598],{"className":3574},[652],[572,3576],{"className":3577,"style":657},[656],[572,3579,605],{"className":3580,"style":663},[661,662]," negativ.",{"title":3583,"searchDepth":3584,"depth":3584,"links":3585},"",2,[3586,3587,3588,3589],{"id":560,"depth":3584,"text":561},{"id":1204,"depth":3584,"text":1205},{"id":2094,"depth":3584,"text":2095},{"id":3022,"depth":3584,"text":3023},[3591,3594,3597,3600,3602,3604,3606],{"lhs":3592,"rhs":3593},"tan(x)","sin(x)\u002Fcos(x)",{"lhs":3595,"rhs":3596},"(a\u002Fsqrt(a^2 + b^2)) \u002F (b\u002Fsqrt(a^2 + b^2))","a\u002Fb",{"lhs":3598,"rhs":3599},"0.6\u002F0.8","0.75",{"lhs":3601,"rhs":3599},"tan(asin(0.6))",{"lhs":3603,"rhs":2553},"sin(45*pi\u002F180) \u002F cos(45*pi\u002F180)",{"lhs":3605,"rhs":802},"cos(90*pi\u002F180)",{"lhs":3607,"rhs":3608},"sign(tan(120*pi\u002F180))","-1","\\cos \\alpha \\neq 0,\\ \\text{d.h.}\\ \\alpha \\neq 90^\\circ + k \\cdot 180^\\circ,\\ k \\in \\mathbb{Z}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\cos \\alpha \\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=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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 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separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha \\neq 90^\\circ + k \\cdot 180^\\circ,\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\" style=\"margin-right:0.0037em;\">α\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:0.7574em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">9\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\tan \\alpha = \\frac{\\sin \\alpha}{\\cos \\alpha}\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:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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:2.0309em;vertical-align:-0.686em;\">\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:1.3449em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","jVUvhEEYSs9nHOnGOmn2NYacWXBr1kUvZVvmkE6Xs5Y",[3707,3710,3713,3716],{"stem":3708,"title":3709,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fkosinus-im-rechtwinkligen-dreieck","Kosinus im rechtwinkligen Dreieck",{"stem":3711,"title":3712,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck","Sinus im rechtwinkligen Dreieck",{"stem":3714,"title":3715,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftangens-im-rechtwinkligen-dreieck","Tangens im rechtwinkligen Dreieck",{"stem":3717,"title":3718,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftrigonometrischer-pythagoras","Trigonometrischer Pythagoras",1793824263260]