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x}",[572,1140,1142,1172],{"className":1141,"ariaHidden":621},[620],[572,1143,1145,1148,1151,1154,1157,1160,1163,1166,1169],{"className":1144},[625],[572,1146],{"className":1147,"style":630},[629],[572,1149,837],{"className":1150},[634],[572,1152,601],{"className":1153},[638],[572,1155,605],{"className":1156},[642],[572,1158,608],{"className":1159},[642,646],[572,1161,611],{"className":1162},[650],[572,1164],{"className":1165,"style":920},[742],[572,1167,966],{"className":1168},[924],[572,1170],{"className":1171,"style":920},[742],[572,1173,1175,1179],{"className":1174},[625],[572,1176],{"className":1177,"style":1178},[629],"height:2.2885em;vertical-align:-0.7924em;",[572,1180,1182,1185,1350],{"className":1181},[642],[572,1183],{"className":1184},[638,983],[572,1186,1188],{"className":1187},[850],[572,1189,1191,1341],{"className":1190},[883,990],[572,1192,1194,1338],{"className":1193},[887],[572,1195,1198,1262,1270],{"className":1196,"style":1197},[891],"height:1.4961em;",[572,1199,1201,1204],{"style":1200},"top:-2.2909em;",[572,1202],{"className":1203,"style":1004},[899],[572,1205,1207,1210,1214,1218,1221,1224,1227,1256,1259],{"className":1206},[642],[572,1208,854],{"className":1209},[642],[572,1211],{"className":1212,"style":1213},[742],"margin-right:0.2222em;",[572,1215,1103],{"className":1216},[1217],"mbin",[572,1219],{"className":1220,"style":1213},[742],[572,1222,605],{"className":1223},[642],[572,1225],{"className":1226,"style":743},[742],[572,1228,1230,1233],{"className":1229},[634],[572,1231,837],{"className":1232},[634],[572,1234,1236],{"className":1235},[879],[572,1237,1239],{"className":1238},[883],[572,1240,1242],{"className":1241},[887],[572,1243,1245],{"className":1244,"style":892},[891],[572,1246,1247,1250],{"style":895},[572,1248],{"className":1249,"style":900},[899],[572,1251,1253],{"className":1252},[904,905,906,907],[572,1254,842],{"className":1255},[642,907],[572,1257],{"className":1258,"style":743},[742],[572,1260,608],{"className":1261},[642,646],[572,1263,1264,1267],{"style":1016},[572,1265],{"className":1266,"style":1004},[899],[572,1268],{"className":1269,"style":1024},[1023],[572,1271,1273,1276],{"style":1272},"top:-3.677em;",[572,1274],{"className":1275,"style":1004},[899],[572,1277,1279,1282,1285,1288,1291,1294,1297,1300,1303,1332,1335],{"className":1278},[642],[572,1280,605],{"className":1281},[642],[572,1283],{"className":1284,"style":743},[742],[572,1286,837],{"className":1287},[634],[572,1289],{"className":1290,"style":743},[742],[572,1292,608],{"className":1293},[642,646],[572,1295],{"className":1296,"style":1213},[742],[572,1298,1103],{"className":1299},[1217],[572,1301],{"className":1302,"style":1213},[742],[572,1304,1306,1309],{"className":1305},[634],[572,1307,837],{"className":1308},[634],[572,1310,1312],{"className":1311},[879],[572,1313,1315],{"className":1314},[883],[572,1316,1318],{"className":1317},[887],[572,1319,1321],{"className":1320,"style":892},[891],[572,1322,1323,1326],{"style":895},[572,1324],{"className":1325,"style":900},[899],[572,1327,1329],{"className":1328},[904,905,906,907],[572,1330,605],{"className":1331},[642,907],[572,1333],{"className":1334,"style":743},[742],[572,1336,608],{"className":1337},[642,646],[572,1339,1044],{"className":1340},[1043],[572,1342,1344],{"className":1343},[887],[572,1345,1348],{"className":1346,"style":1347},[891],"height:0.7924em;",[572,1349],{},[572,1351],{"className":1352},[650,983],[564,1354,1355],{},"Anwendungen:",[1357,1358,1359,1757,2056],"ul",{},[1360,1361,1362,1363,651,1436,1509,1510,1756],"li",{},"Umrechnen von ",[572,1364,1366,1390],{"className":1365},[575],[572,1367,1369],{"className":1368},[579],[581,1370,1371],{"xmlns":583},[585,1372,1373,1387],{},[588,1374,1375,1385],{},[831,1376,1377,1383],{},[588,1378,1379,1381],{},[591,1380,593],{},[595,1382,597],{},[603,1384,605],{},[591,1386,608],{},[613,1388,1389],{"encoding":615},"\\sin^3 x",[572,1391,1393],{"className":1392,"ariaHidden":621},[620],[572,1394,1396,1400,1430,1433],{"className":1395},[625],[572,1397],{"className":1398,"style":1399},[629],"height:0.8719em;",[572,1401,1403,1406],{"className":1402},[634],[572,1404,593],{"className":1405},[634],[572,1407,1409],{"className":1408},[879],[572,1410,1412],{"className":1411},[883],[572,1413,1415],{"className":1414},[887],[572,1416,1418],{"className":1417,"style":1399},[891],[572,1419,1421,1424],{"style":1420},"top:-3.1208em;margin-right:0.05em;",[572,1422],{"className":1423,"style":900},[899],[572,1425,1427],{"className":1426},[904,905,906,907],[572,1428,605],{"className":1429},[642,907],[572,1431],{"className":1432,"style":743},[742],[572,1434,608],{"className":1435},[642,646],[572,1437,1439,1463],{"className":1438},[575],[572,1440,1442],{"className":1441},[579],[581,1443,1444],{"xmlns":583},[585,1445,1446,1460],{},[588,1447,1448,1458],{},[831,1449,1450,1456],{},[588,1451,1452,1454],{},[591,1453,666],{},[595,1455,597],{},[603,1457,605],{},[591,1459,608],{},[613,1461,1462],{"encoding":615},"\\cos^3 x",[572,1464,1466],{"className":1465,"ariaHidden":621},[620],[572,1467,1469,1473,1503,1506],{"className":1468},[625],[572,1470],{"className":1471,"style":1472},[629],"height:0.8141em;",[572,1474,1476,1479],{"className":1475},[634],[572,1477,666],{"className":1478},[634],[572,1480,1482],{"className":1481},[879],[572,1483,1485],{"className":1484},[883],[572,1486,1488],{"className":1487},[887],[572,1489,1491],{"className":1490,"style":1472},[891],[572,1492,1494,1497],{"style":1493},"top:-3.063em;margin-right:0.05em;",[572,1495],{"className":1496,"style":900},[899],[572,1498,1500],{"className":1499},[904,905,906,907],[572,1501,605],{"className":1502},[642,907],[572,1504],{"className":1505,"style":743},[742],[572,1507,608],{"className":1508},[642,646]," in lineare Ausdrücke, etwa für Integrale: ",[572,1511,1513,1575],{"className":1512},[575],[572,1514,1516],{"className":1515},[579],[581,1517,1518],{"xmlns":583},[585,1519,1520,1572],{},[588,1521,1522,1532,1534,1536,1543],{},[831,1523,1524,1530],{},[588,1525,1526,1528],{},[591,1527,666],{},[595,1529,597],{},[603,1531,605],{},[591,1533,608],{},[595,1535,966],{},[850,1537,1538,1540],{},[603,1539,854],{},[603,1541,1542],{},"4",[588,1544,1545,1547,1549,1551,1553,1555,1557,1559,1562,1564,1566,1568,1570],{},[595,1546,601],{"fence":621},[591,1548,666],{},[595,1550,597],{},[595,1552,601],{"stretchy":600},[603,1554,605],{},[591,1556,608],{},[595,1558,611],{"stretchy":600},[595,1560,1561],{},"+",[603,1563,605],{},[591,1565,666],{},[595,1567,597],{},[591,1569,608],{},[595,1571,611],{"fence":621},[613,1573,1574],{"encoding":615},"\\cos^3 x = \\frac{1}{4}\\left(\\cos(3x) + 3\\cos x\\right)",[572,1576,1578,1628],{"className":1577,"ariaHidden":621},[620],[572,1579,1581,1584,1613,1616,1619,1622,1625],{"className":1580},[625],[572,1582],{"className":1583,"style":1472},[629],[572,1585,1587,1590],{"className":1586},[634],[572,1588,666],{"className":1589},[634],[572,1591,1593],{"className":1592},[879],[572,1594,1596],{"className":1595},[883],[572,1597,1599],{"className":1598},[887],[572,1600,1602],{"className":1601,"style":1472},[891],[572,1603,1604,1607],{"style":1493},[572,1605],{"className":1606,"style":900},[899],[572,1608,1610],{"className":1609},[904,905,906,907],[572,1611,605],{"className":1612},[642,907],[572,1614],{"className":1615,"style":743},[742],[572,1617,608],{"className":1618},[642,646],[572,1620],{"className":1621,"style":920},[742],[572,1623,966],{"className":1624},[924],[572,1626],{"className":1627,"style":920},[742],[572,1629,1631,1634,1702,1705],{"className":1630},[625],[572,1632],{"className":1633,"style":976},[629],[572,1635,1637,1640,1699],{"className":1636},[642],[572,1638],{"className":1639},[638,983],[572,1641,1643],{"className":1642},[850],[572,1644,1646,1691],{"className":1645},[883,990],[572,1647,1649,1688],{"className":1648},[887],[572,1650,1652,1666,1674],{"className":1651,"style":997},[891],[572,1653,1654,1657],{"style":1000},[572,1655],{"className":1656,"style":1004},[899],[572,1658,1660],{"className":1659},[904,905,906,907],[572,1661,1663],{"className":1662},[642,907],[572,1664,1542],{"className":1665},[642,907],[572,1667,1668,1671],{"style":1016},[572,1669],{"className":1670,"style":1004},[899],[572,1672],{"className":1673,"style":1024},[1023],[572,1675,1676,1679],{"style":1027},[572,1677],{"className":1678,"style":1004},[899],[572,1680,1682],{"className":1681},[904,905,906,907],[572,1683,1685],{"className":1684},[642,907],[572,1686,854],{"className":1687},[642,907],[572,1689,1044],{"className":1690},[1043],[572,1692,1694],{"className":1693},[887],[572,1695,1697],{"className":1696,"style":1051},[891],[572,1698],{},[572,1700],{"className":1701},[650,983],[572,1703],{"className":1704,"style":743},[742],[572,1706,1709,1714,1717,1720,1723,1726,1729,1732,1735,1738,1741,1744,1747,1750,1753],{"className":1707},[1708],"minner",[572,1710,601],{"className":1711,"style":1713},[638,1712],"delimcenter","top:0em;",[572,1715,666],{"className":1716},[634],[572,1718,601],{"className":1719},[638],[572,1721,605],{"className":1722},[642],[572,1724,608],{"className":1725},[642,646],[572,1727,611],{"className":1728},[650],[572,1730],{"className":1731,"style":1213},[742],[572,1733,1561],{"className":1734},[1217],[572,1736],{"className":1737,"style":1213},[742],[572,1739,605],{"className":1740},[642],[572,1742],{"className":1743,"style":743},[742],[572,1745,666],{"className":1746},[634],[572,1748],{"className":1749,"style":743},[742],[572,1751,608],{"className":1752},[642,646],[572,1754,611],{"className":1755,"style":1713},[650,1712],".",[1360,1758,1759,1760,1810,1811,1814,1815,1993,1994,1756],{},"Die Formel für ",[572,1761,1763,1786],{"className":1762},[575],[572,1764,1766],{"className":1765},[579],[581,1767,1768],{"xmlns":583},[585,1769,1770,1784],{},[588,1771,1772,1774,1776,1778,1780,1782],{},[591,1773,666],{},[595,1775,597],{},[595,1777,601],{"stretchy":600},[603,1779,605],{},[591,1781,608],{},[595,1783,611],{"stretchy":600},[613,1785,679],{"encoding":615},[572,1787,1789],{"className":1788,"ariaHidden":621},[620],[572,1790,1792,1795,1798,1801,1804,1807],{"className":1791},[625],[572,1793],{"className":1794,"style":630},[629],[572,1796,666],{"className":1797},[634],[572,1799,601],{"className":1800},[638],[572,1802,605],{"className":1803},[642],[572,1805,608],{"className":1806},[642,646],[572,1808,611],{"className":1809},[650]," ist das ",[568,1812,1813],{},"Tschebyschow-Polynom"," ",[572,1816,1818,1861],{"className":1817},[575],[572,1819,1821],{"className":1820},[579],[581,1822,1823],{"xmlns":583},[585,1824,1825,1858],{},[588,1826,1827,1835,1837,1840,1842,1844,1846,1852,1854,1856],{},[1828,1829,1830,1833],"msub",{},[591,1831,1832],{},"T",[603,1834,605],{},[595,1836,601],{"stretchy":600},[591,1838,1839],{},"t",[595,1841,611],{"stretchy":600},[595,1843,966],{},[603,1845,1542],{},[831,1847,1848,1850],{},[591,1849,1839],{},[603,1851,605],{},[595,1853,1103],{},[603,1855,605],{},[591,1857,1839],{},[613,1859,1860],{"encoding":615},"T_3(t) = 4t^3 - 3t",[572,1862,1864,1932,1980],{"className":1863,"ariaHidden":621},[620],[572,1865,1867,1870,1914,1917,1920,1923,1926,1929],{"className":1866},[625],[572,1868],{"className":1869,"style":630},[629],[572,1871,1873,1877],{"className":1872},[642],[572,1874,1832],{"className":1875,"style":1876},[642,646],"margin-right:0.1389em;",[572,1878,1880],{"className":1879},[879],[572,1881,1883,1905],{"className":1882},[883,990],[572,1884,1886,1902],{"className":1885},[887],[572,1887,1890],{"className":1888,"style":1889},[891],"height:0.3011em;",[572,1891,1893,1896],{"style":1892},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[572,1894],{"className":1895,"style":900},[899],[572,1897,1899],{"className":1898},[904,905,906,907],[572,1900,605],{"className":1901},[642,907],[572,1903,1044],{"className":1904},[1043],[572,1906,1908],{"className":1907},[887],[572,1909,1912],{"className":1910,"style":1911},[891],"height:0.15em;",[572,1913],{},[572,1915,601],{"className":1916},[638],[572,1918,1839],{"className":1919},[642,646],[572,1921,611],{"className":1922},[650],[572,1924],{"className":1925,"style":920},[742],[572,1927,966],{"className":1928},[924],[572,1930],{"className":1931,"style":920},[742],[572,1933,1935,1939,1942,1971,1974,1977],{"className":1934},[625],[572,1936],{"className":1937,"style":1938},[629],"height:0.8974em;vertical-align:-0.0833em;",[572,1940,1542],{"className":1941},[642],[572,1943,1945,1948],{"className":1944},[642],[572,1946,1839],{"className":1947},[642,646],[572,1949,1951],{"className":1950},[879],[572,1952,1954],{"className":1953},[883],[572,1955,1957],{"className":1956},[887],[572,1958,1960],{"className":1959,"style":1472},[891],[572,1961,1962,1965],{"style":1493},[572,1963],{"className":1964,"style":900},[899],[572,1966,1968],{"className":1967},[904,905,906,907],[572,1969,605],{"className":1970},[642,907],[572,1972],{"className":1973,"style":1213},[742],[572,1975,1103],{"className":1976},[1217],[572,1978],{"className":1979,"style":1213},[742],[572,1981,1983,1987,1990],{"className":1982},[625],[572,1984],{"className":1985,"style":1986},[629],"height:0.6444em;",[572,1988,605],{"className":1989},[642],[572,1991,1839],{"className":1992},[642,646]," an der Stelle ",[572,1995,1997,2019],{"className":1996},[575],[572,1998,2000],{"className":1999},[579],[581,2001,2002],{"xmlns":583},[585,2003,2004,2016],{},[588,2005,2006,2008,2010,2012,2014],{},[591,2007,1839],{},[595,2009,966],{},[591,2011,666],{},[595,2013,597],{},[591,2015,608],{},[613,2017,2018],{"encoding":615},"t = \\cos x",[572,2020,2022,2041],{"className":2021,"ariaHidden":621},[620],[572,2023,2025,2029,2032,2035,2038],{"className":2024},[625],[572,2026],{"className":2027,"style":2028},[629],"height:0.6151em;",[572,2030,1839],{"className":2031},[642,646],[572,2033],{"className":2034,"style":920},[742],[572,2036,966],{"className":2037},[924],[572,2039],{"className":2040,"style":920},[742],[572,2042,2044,2047,2050,2053],{"className":2043},[625],[572,2045],{"className":2046,"style":778},[629],[572,2048,666],{"className":2049},[634],[572,2051],{"className":2052,"style":743},[742],[572,2054,608],{"className":2055},[642,646],[1360,2057,2058],{},"Die Dreiteilung eines Winkels führt auf eine kubische Gleichung. Daraus folgt, dass sie mit Zirkel und Lineal im Allgemeinen nicht möglich ist.",[559,2060,2062],{"id":2061},"herleitung","Herleitung",[564,2064,2065,2066,2139],{},"Mit dem Additionstheorem für ",[572,2067,2069,2097],{"className":2068},[575],[572,2070,2072],{"className":2071},[579],[581,2073,2074],{"xmlns":583},[585,2075,2076,2094],{},[588,2077,2078,2080,2082,2084,2086,2088,2090,2092],{},[591,2079,593],{},[595,2081,597],{},[595,2083,601],{"stretchy":600},[603,2085,842],{},[591,2087,608],{},[595,2089,1561],{},[591,2091,608],{},[595,2093,611],{"stretchy":600},[613,2095,2096],{"encoding":615},"\\sin(2x + x)",[572,2098,2100,2127],{"className":2099,"ariaHidden":621},[620],[572,2101,2103,2106,2109,2112,2115,2118,2121,2124],{"className":2102},[625],[572,2104],{"className":2105,"style":630},[629],[572,2107,593],{"className":2108},[634],[572,2110,601],{"className":2111},[638],[572,2113,842],{"className":2114},[642],[572,2116,608],{"className":2117},[642,646],[572,2119],{"className":2120,"style":1213},[742],[572,2122,1561],{"className":2123},[1217],[572,2125],{"className":2126,"style":1213},[742],[572,2128,2130,2133,2136],{"className":2129},[625],[572,2131],{"className":2132,"style":630},[629],[572,2134,608],{"className":2135},[642,646],[572,2137,611],{"className":2138},[650]," und den Doppelwinkelformeln:",[572,2141,2143],{"className":2142},[1061],[572,2144,2146,2262],{"className":2145},[575],[572,2147,2149],{"className":2148},[579],[581,2150,2151],{"xmlns":583,"display":1070},[585,2152,2153,2259],{},[588,2154,2155,2157,2159,2161,2163,2165,2167,2169,2171,2173,2175,2177,2179,2181,2183,2185,2187,2189,2191,2193,2195,2197,2199,2201,2203,2205,2207,2209,2211,2213,2215,2217,2227,2229,2231,2233,2235,2237,2239,2249,2251,2253,2255,2257],{},[591,2156,593],{},[595,2158,597],{},[595,2160,601],{"stretchy":600},[603,2162,605],{},[591,2164,608],{},[595,2166,611],{"stretchy":600},[595,2168,966],{},[591,2170,593],{},[595,2172,597],{},[595,2174,601],{"stretchy":600},[603,2176,842],{},[591,2178,608],{},[595,2180,611],{"stretchy":600},[591,2182,666],{},[595,2184,597],{},[591,2186,608],{},[595,2188,1561],{},[591,2190,666],{},[595,2192,597],{},[595,2194,601],{"stretchy":600},[603,2196,842],{},[591,2198,608],{},[595,2200,611],{"stretchy":600},[591,2202,593],{},[595,2204,597],{},[591,2206,608],{},[595,2208,966],{},[603,2210,842],{},[591,2212,593],{},[595,2214,597],{},[591,2216,608],{},[831,2218,2219,2225],{},[588,2220,2221,2223],{},[591,2222,666],{},[595,2224,597],{},[603,2226,842],{},[591,2228,608],{},[595,2230,1561],{},[595,2232,601],{"stretchy":600},[603,2234,854],{},[595,2236,1103],{},[603,2238,842],{},[831,2240,2241,2247],{},[588,2242,2243,2245],{},[591,2244,593],{},[595,2246,597],{},[603,2248,842],{},[591,2250,608],{},[595,2252,611],{"stretchy":600},[591,2254,593],{},[595,2256,597],{},[591,2258,608],{},[613,2260,2261],{"encoding":615},"\\sin(3x) = \\sin(2x)\\cos x + \\cos(2x)\\sin x = 2\\sin x \\cos^2 x + (1 - 2\\sin^2 x)\\sin x",[572,2263,2265,2295,2337,2379,2450,2471],{"className":2264,"ariaHidden":621},[620],[572,2266,2268,2271,2274,2277,2280,2283,2286,2289,2292],{"className":2267},[625],[572,2269],{"className":2270,"style":630},[629],[572,2272,593],{"className":2273},[634],[572,2275,601],{"className":2276},[638],[572,2278,605],{"className":2279},[642],[572,2281,608],{"className":2282},[642,646],[572,2284,611],{"className":2285},[650],[572,2287],{"className":2288,"style":920},[742],[572,2290,966],{"className":2291},[924],[572,2293],{"className":2294,"style":920},[742],[572,2296,2298,2301,2304,2307,2310,2313,2316,2319,2322,2325,2328,2331,2334],{"className":2297},[625],[572,2299],{"className":2300,"style":630},[629],[572,2302,593],{"className":2303},[634],[572,2305,601],{"className":2306},[638],[572,2308,842],{"className":2309},[642],[572,2311,608],{"className":2312},[642,646],[572,2314,611],{"className":2315},[650],[572,2317],{"className":2318,"style":743},[742],[572,2320,666],{"className":2321},[634],[572,2323],{"className":2324,"style":743},[742],[572,2326,608],{"className":2327},[642,646],[572,2329],{"className":2330,"style":1213},[742],[572,2332,1561],{"className":2333},[1217],[572,2335],{"className":2336,"style":1213},[742],[572,2338,2340,2343,2346,2349,2352,2355,2358,2361,2364,2367,2370,2373,2376],{"className":2339},[625],[572,2341],{"className":2342,"style":630},[629],[572,2344,666],{"className":2345},[634],[572,2347,601],{"className":2348},[638],[572,2350,842],{"className":2351},[642],[572,2353,608],{"className":2354},[642,646],[572,2356,611],{"className":2357},[650],[572,2359],{"className":2360,"style":743},[742],[572,2362,593],{"className":2363},[634],[572,2365],{"className":2366,"style":743},[742],[572,2368,608],{"className":2369},[642,646],[572,2371],{"className":2372,"style":920},[742],[572,2374,966],{"className":2375},[924],[572,2377],{"className":2378,"style":920},[742],[572,2380,2382,2386,2389,2392,2395,2398,2401,2404,2435,2438,2441,2444,2447],{"className":2381},[625],[572,2383],{"className":2384,"style":2385},[629],"height:0.9474em;vertical-align:-0.0833em;",[572,2387,842],{"className":2388},[642],[572,2390],{"className":2391,"style":743},[742],[572,2393,593],{"className":2394},[634],[572,2396],{"className":2397,"style":743},[742],[572,2399,608],{"className":2400},[642,646],[572,2402],{"className":2403,"style":743},[742],[572,2405,2407,2410],{"className":2406},[634],[572,2408,666],{"className":2409},[634],[572,2411,2413],{"className":2412},[879],[572,2414,2416],{"className":2415},[883],[572,2417,2419],{"className":2418},[887],[572,2420,2423],{"className":2421,"style":2422},[891],"height:0.8641em;",[572,2424,2426,2429],{"style":2425},"top:-3.113em;margin-right:0.05em;",[572,2427],{"className":2428,"style":900},[899],[572,2430,2432],{"className":2431},[904,905,906,907],[572,2433,842],{"className":2434},[642,907],[572,2436],{"className":2437,"style":743},[742],[572,2439,608],{"className":2440},[642,646],[572,2442],{"className":2443,"style":1213},[742],[572,2445,1561],{"className":2446},[1217],[572,2448],{"className":2449,"style":1213},[742],[572,2451,2453,2456,2459,2462,2465,2468],{"className":2452},[625],[572,2454],{"className":2455,"style":630},[629],[572,2457,601],{"className":2458},[638],[572,2460,854],{"className":2461},[642],[572,2463],{"className":2464,"style":1213},[742],[572,2466,1103],{"className":2467},[1217],[572,2469],{"className":2470,"style":1213},[742],[572,2472,2474,2478,2481,2484,2513,2516,2519,2522,2525,2528,2531],{"className":2473},[625],[572,2475],{"className":2476,"style":2477},[629],"height:1.1219em;vertical-align:-0.25em;",[572,2479,842],{"className":2480},[642],[572,2482],{"className":2483,"style":743},[742],[572,2485,2487,2490],{"className":2486},[634],[572,2488,593],{"className":2489},[634],[572,2491,2493],{"className":2492},[879],[572,2494,2496],{"className":2495},[883],[572,2497,2499],{"className":2498},[887],[572,2500,2502],{"className":2501,"style":1399},[891],[572,2503,2504,2507],{"style":1420},[572,2505],{"className":2506,"style":900},[899],[572,2508,2510],{"className":2509},[904,905,906,907],[572,2511,842],{"className":2512},[642,907],[572,2514],{"className":2515,"style":743},[742],[572,2517,608],{"className":2518},[642,646],[572,2520,611],{"className":2521},[650],[572,2523],{"className":2524,"style":743},[742],[572,2526,593],{"className":2527},[634],[572,2529],{"className":2530,"style":743},[742],[572,2532,608],{"className":2533},[642,646],[564,2535,2536,2537,2695,2696,2816,2817,3035],{},"Mit ",[572,2538,2540,2582],{"className":2539},[575],[572,2541,2543],{"className":2542},[579],[581,2544,2545],{"xmlns":583},[585,2546,2547,2579],{},[588,2548,2549,2559,2561,2563,2565,2567,2577],{},[831,2550,2551,2557],{},[588,2552,2553,2555],{},[591,2554,666],{},[595,2556,597],{},[603,2558,842],{},[591,2560,608],{},[595,2562,966],{},[603,2564,854],{},[595,2566,1103],{},[831,2568,2569,2575],{},[588,2570,2571,2573],{},[591,2572,593],{},[595,2574,597],{},[603,2576,842],{},[591,2578,608],{},[613,2580,2581],{"encoding":615},"\\cos^2 x = 1 - \\sin^2 x",[572,2583,2585,2635,2654],{"className":2584,"ariaHidden":621},[620],[572,2586,2588,2591,2620,2623,2626,2629,2632],{"className":2587},[625],[572,2589],{"className":2590,"style":1472},[629],[572,2592,2594,2597],{"className":2593},[634],[572,2595,666],{"className":2596},[634],[572,2598,2600],{"className":2599},[879],[572,2601,2603],{"className":2602},[883],[572,2604,2606],{"className":2605},[887],[572,2607,2609],{"className":2608,"style":1472},[891],[572,2610,2611,2614],{"style":1493},[572,2612],{"className":2613,"style":900},[899],[572,2615,2617],{"className":2616},[904,905,906,907],[572,2618,842],{"className":2619},[642,907],[572,2621],{"className":2622,"style":743},[742],[572,2624,608],{"className":2625},[642,646],[572,2627],{"className":2628,"style":920},[742],[572,2630,966],{"className":2631},[924],[572,2633],{"className":2634,"style":920},[742],[572,2636,2638,2642,2645,2648,2651],{"className":2637},[625],[572,2639],{"className":2640,"style":2641},[629],"height:0.7278em;vertical-align:-0.0833em;",[572,2643,854],{"className":2644},[642],[572,2646],{"className":2647,"style":1213},[742],[572,2649,1103],{"className":2650},[1217],[572,2652],{"className":2653,"style":1213},[742],[572,2655,2657,2660,2689,2692],{"className":2656},[625],[572,2658],{"className":2659,"style":1399},[629],[572,2661,2663,2666],{"className":2662},[634],[572,2664,593],{"className":2665},[634],[572,2667,2669],{"className":2668},[879],[572,2670,2672],{"className":2671},[883],[572,2673,2675],{"className":2674},[887],[572,2676,2678],{"className":2677,"style":1399},[891],[572,2679,2680,2683],{"style":1420},[572,2681],{"className":2682,"style":900},[899],[572,2684,2686],{"className":2685},[904,905,906,907],[572,2687,842],{"className":2688},[642,907],[572,2690],{"className":2691,"style":743},[742],[572,2693,608],{"className":2694},[642,646]," ergibt sich ",[572,2697,2699,2735],{"className":2698},[575],[572,2700,2702],{"className":2701},[579],[581,2703,2704],{"xmlns":583},[585,2705,2706,2732],{},[588,2707,2708,2710,2712,2714,2716,2718,2720,2730],{},[603,2709,605],{},[591,2711,593],{},[595,2713,597],{},[591,2715,608],{},[595,2717,1103],{},[603,2719,1542],{},[831,2721,2722,2728],{},[588,2723,2724,2726],{},[591,2725,593],{},[595,2727,597],{},[603,2729,605],{},[591,2731,608],{},[613,2733,2734],{"encoding":615},"3\\sin x - 4\\sin^3 x",[572,2736,2738,2769],{"className":2737,"ariaHidden":621},[620],[572,2739,2741,2745,2748,2751,2754,2757,2760,2763,2766],{"className":2740},[625],[572,2742],{"className":2743,"style":2744},[629],"height:0.7512em;vertical-align:-0.0833em;",[572,2746,605],{"className":2747},[642],[572,2749],{"className":2750,"style":743},[742],[572,2752,593],{"className":2753},[634],[572,2755],{"className":2756,"style":743},[742],[572,2758,608],{"className":2759},[642,646],[572,2761],{"className":2762,"style":1213},[742],[572,2764,1103],{"className":2765},[1217],[572,2767],{"className":2768,"style":1213},[742],[572,2770,2772,2775,2778,2781,2810,2813],{"className":2771},[625],[572,2773],{"className":2774,"style":1399},[629],[572,2776,1542],{"className":2777},[642],[572,2779],{"className":2780,"style":743},[742],[572,2782,2784,2787],{"className":2783},[634],[572,2785,593],{"className":2786},[634],[572,2788,2790],{"className":2789},[879],[572,2791,2793],{"className":2792},[883],[572,2794,2796],{"className":2795},[887],[572,2797,2799],{"className":2798,"style":1399},[891],[572,2800,2801,2804],{"style":1420},[572,2802],{"className":2803,"style":900},[899],[572,2805,2807],{"className":2806},[904,905,906,907],[572,2808,605],{"className":2809},[642,907],[572,2811],{"className":2812,"style":743},[742],[572,2814,608],{"className":2815},[642,646],". Für den Kosinus geht man analog vor. Alternativ vergleicht man Real- und Imaginärteil von ",[572,2818,2820,2887],{"className":2819},[575],[572,2821,2823],{"className":2822},[579],[581,2824,2825],{"xmlns":583},[585,2826,2827,2884],{},[588,2828,2829,2831,2833,2835,2837,2839,2842,2844,2846,2848,2854,2856,2858,2860,2862,2864,2866,2868,2870,2872,2874,2876,2878,2880,2882],{},[595,2830,601],{"stretchy":600},[591,2832,666],{},[595,2834,597],{},[591,2836,608],{},[595,2838,1561],{},[591,2840,2841],{"mathvariant":847},"i",[591,2843,593],{},[595,2845,597],{},[591,2847,608],{},[831,2849,2850,2852],{},[595,2851,611],{"stretchy":600},[603,2853,605],{},[595,2855,966],{},[591,2857,666],{},[595,2859,597],{},[595,2861,601],{"stretchy":600},[603,2863,605],{},[591,2865,608],{},[595,2867,611],{"stretchy":600},[595,2869,1561],{},[591,2871,2841],{"mathvariant":847},[591,2873,593],{},[595,2875,597],{},[595,2877,601],{"stretchy":600},[603,2879,605],{},[591,2881,608],{},[595,2883,611],{"stretchy":600},[613,2885,2886],{"encoding":615},"(\\cos x + \\mathrm{i} \\sin x)^3 = \\cos(3x) + \\mathrm{i}\\sin(3x)",[572,2888,2890,2917,2978,3008],{"className":2889,"ariaHidden":621},[620],[572,2891,2893,2896,2899,2902,2905,2908,2911,2914],{"className":2892},[625],[572,2894],{"className":2895,"style":630},[629],[572,2897,601],{"className":2898},[638],[572,2900,666],{"className":2901},[634],[572,2903],{"className":2904,"style":743},[742],[572,2906,608],{"className":2907},[642,646],[572,2909],{"className":2910,"style":1213},[742],[572,2912,1561],{"className":2913},[1217],[572,2915],{"className":2916,"style":1213},[742],[572,2918,2920,2924,2928,2931,2934,2937,2940,2969,2972,2975],{"className":2919},[625],[572,2921],{"className":2922,"style":2923},[629],"height:1.0641em;vertical-align:-0.25em;",[572,2925,2841],{"className":2926},[642,2927],"mathrm",[572,2929],{"className":2930,"style":743},[742],[572,2932,593],{"className":2933},[634],[572,2935],{"className":2936,"style":743},[742],[572,2938,608],{"className":2939},[642,646],[572,2941,2943,2946],{"className":2942},[650],[572,2944,611],{"className":2945},[650],[572,2947,2949],{"className":2948},[879],[572,2950,2952],{"className":2951},[883],[572,2953,2955],{"className":2954},[887],[572,2956,2958],{"className":2957,"style":1472},[891],[572,2959,2960,2963],{"style":1493},[572,2961],{"className":2962,"style":900},[899],[572,2964,2966],{"className":2965},[904,905,906,907],[572,2967,605],{"className":2968},[642,907],[572,2970],{"className":2971,"style":920},[742],[572,2973,966],{"className":2974},[924],[572,2976],{"className":2977,"style":920},[742],[572,2979,2981,2984,2987,2990,2993,2996,2999,3002,3005],{"className":2980},[625],[572,2982],{"className":2983,"style":630},[629],[572,2985,666],{"className":2986},[634],[572,2988,601],{"className":2989},[638],[572,2991,605],{"className":2992},[642],[572,2994,608],{"className":2995},[642,646],[572,2997,611],{"className":2998},[650],[572,3000],{"className":3001,"style":1213},[742],[572,3003,1561],{"className":3004},[1217],[572,3006],{"className":3007,"style":1213},[742],[572,3009,3011,3014,3017,3020,3023,3026,3029,3032],{"className":3010},[625],[572,3012],{"className":3013,"style":630},[629],[572,3015,2841],{"className":3016},[642,2927],[572,3018],{"className":3019,"style":743},[742],[572,3021,593],{"className":3022},[634],[572,3024,601],{"className":3025},[638],[572,3027,605],{"className":3028},[642],[572,3030,608],{"className":3031},[642,646],[572,3033,611],{"className":3034},[650]," (Formel von Moivre).",[559,3037,3039],{"id":3038},"beispiele","Beispiele",[564,3041,2536,3042,3131,3132,1057],{},[572,3043,3045,3069],{"className":3044},[575],[572,3046,3048],{"className":3047},[579],[581,3049,3050],{"xmlns":583},[585,3051,3052,3066],{},[588,3053,3054,3056,3058],{},[591,3055,608],{},[595,3057,966],{},[831,3059,3060,3063],{},[603,3061,3062],{},"60",[595,3064,3065],{},"∘",[613,3067,3068],{"encoding":615},"x = 60^\\circ",[572,3070,3072,3090],{"className":3071,"ariaHidden":621},[620],[572,3073,3075,3078,3081,3084,3087],{"className":3074},[625],[572,3076],{"className":3077,"style":778},[629],[572,3079,608],{"className":3080},[642,646],[572,3082],{"className":3083,"style":920},[742],[572,3085,966],{"className":3086},[924],[572,3088],{"className":3089,"style":920},[742],[572,3091,3093,3097,3101],{"className":3092},[625],[572,3094],{"className":3095,"style":3096},[629],"height:0.6741em;",[572,3098,3100],{"className":3099},[642],"6",[572,3102,3104,3108],{"className":3103},[642],[572,3105,3107],{"className":3106},[642],"0",[572,3109,3111],{"className":3110},[879],[572,3112,3114],{"className":3113},[883],[572,3115,3117],{"className":3116},[887],[572,3118,3120],{"className":3119,"style":3096},[891],[572,3121,3122,3125],{"style":1493},[572,3123],{"className":3124,"style":900},[899],[572,3126,3128],{"className":3127},[904,905,906,907],[572,3129,3065],{"className":3130},[1217,907],", also ",[572,3133,3135,3161],{"className":3134},[575],[572,3136,3138],{"className":3137},[579],[581,3139,3140],{"xmlns":583},[585,3141,3142,3158],{},[588,3143,3144,3146,3148,3150,3152],{},[591,3145,666],{},[595,3147,597],{},[591,3149,608],{},[595,3151,966],{},[850,3153,3154,3156],{},[603,3155,854],{},[603,3157,842],{},[613,3159,3160],{"encoding":615},"\\cos x = 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180^\\circ = 4 \\cdot \\frac{1}{8} - 3 \\cdot \\frac{1}{2} = -1",[572,3324,3326,3381,3399,3480,3498,3575],{"className":3325,"ariaHidden":621},[620],[572,3327,3329,3333,3336,3339,3343,3372,3375,3378],{"className":3328},[625],[572,3330],{"className":3331,"style":3332},[629],"height:0.7241em;",[572,3334,666],{"className":3335},[634],[572,3337],{"className":3338,"style":743},[742],[572,3340,3342],{"className":3341},[642],"18",[572,3344,3346,3349],{"className":3345},[642],[572,3347,3107],{"className":3348},[642],[572,3350,3352],{"className":3351},[879],[572,3353,3355],{"className":3354},[883],[572,3356,3358],{"className":3357},[887],[572,3359,3361],{"className":3360,"style":3332},[891],[572,3362,3363,3366],{"style":2425},[572,3364],{"className":3365,"style":900},[899],[572,3367,3369],{"className":3368},[904,905,906,907],[572,3370,3065],{"className":3371},[1217,907],[572,3373],{"className":3374,"style":920},[742],[572,3376,966],{"className":3377},[924],[572,3379],{"className":3380,"style":920},[742],[572,3382,3384,3387,3390,3393,3396],{"className":3383},[625],[572,3385],{"className":3386,"style":1986},[629],[572,3388,1542],{"className":3389},[642],[572,3391],{"className":3392,"style":1213},[742],[572,3394,3294],{"className":3395},[1217],[572,3397],{"className":3398,"style":1213},[742],[572,3400,3402,3406,3471,3474,3477],{"className":3401},[625],[572,3403],{"className":3404,"style":3405},[629],"height:2.0074em;vertical-align:-0.686em;",[572,3407,3409,3412,3468],{"className":3408},[642],[572,3410],{"className":3411},[638,983],[572,3413,3415],{"className":3414},[850],[572,3416,3418,3459],{"className":3417},[883,990],[572,3419,3421,3456],{"className":3420},[887],[572,3422,3425,3437,3445],{"className":3423,"style":3424},[891],"height:1.3214em;",[572,3426,3428,3431],{"style":3427},"top:-2.314em;",[572,3429],{"className":3430,"style":1004},[899],[572,3432,3434],{"className":3433},[642],[572,3435,3301],{"className":3436},[642],[572,3438,3439,3442],{"style":1016},[572,3440],{"className":3441,"style":1004},[899],[572,3443],{"className":3444,"style":1024},[1023],[572,3446,3447,3450],{"style":1272},[572,3448],{"className":3449,"style":1004},[899],[572,3451,3453],{"className":3452},[642],[572,3454,854],{"className":3455},[642],[572,3457,1044],{"className":3458},[1043],[572,3460,3462],{"className":3461},[887],[572,3463,3466],{"className":3464,"style":3465},[891],"height:0.686em;",[572,3467],{},[572,3469],{"className":3470},[650,983],[572,3472],{"className":3473,"style":1213},[742],[572,3475,1103],{"className":3476},[1217],[572,3478],{"className":3479,"style":1213},[742],[572,3481,3483,3486,3489,3492,3495],{"className":3482},[625],[572,3484],{"className":3485,"style":1986},[629],[572,3487,605],{"className":3488},[642],[572,3490],{"className":3491,"style":1213},[742],[572,3493,3294],{"className":3494},[1217],[572,3496],{"className":3497,"style":1213},[742],[572,3499,3501,3504,3566,3569,3572],{"className":3500},[625],[572,3502],{"className":3503,"style":3405},[629],[572,3505,3507,3510,3563],{"className":3506},[642],[572,3508],{"className":3509},[638,983],[572,3511,3513],{"className":3512},[850],[572,3514,3516,3555],{"className":3515},[883,990],[572,3517,3519,3552],{"className":3518},[887],[572,3520,3522,3533,3541],{"className":3521,"style":3424},[891],[572,3523,3524,3527],{"style":3427},[572,3525],{"className":3526,"style":1004},[899],[572,3528,3530],{"className":3529},[642],[572,3531,842],{"className":3532},[642],[572,3534,3535,3538],{"style":1016},[572,3536],{"className":3537,"style":1004},[899],[572,3539],{"className":3540,"style":1024},[1023],[572,3542,3543,3546],{"style":1272},[572,3544],{"className":3545,"style":1004},[899],[572,3547,3549],{"className":3548},[642],[572,3550,854],{"className":3551},[642],[572,3553,1044],{"className":3554},[1043],[572,3556,3558],{"className":3557},[887],[572,3559,3561],{"className":3560,"style":3465},[891],[572,3562],{},[572,3564],{"className":3565},[650,983],[572,3567],{"className":3568,"style":920},[742],[572,3570,966],{"className":3571},[924],[572,3573],{"className":3574,"style":920},[742],[572,3576,3578,3581,3584],{"className":3577},[625],[572,3579],{"className":3580,"style":2641},[629],[572,3582,1103],{"className":3583},[642],[572,3585,854],{"className":3586},[642],[564,3588,3589,3590,651,3754,3894,3895,4078,4079,4173,4174,4246],{},"Wegen ",[572,3591,3593,3624],{"className":3592},[575],[572,3594,3596],{"className":3595},[579],[581,3597,3598],{"xmlns":583},[585,3599,3600,3621],{},[588,3601,3602,3604,3606,3613,3615],{},[591,3603,593],{},[595,3605,597],{},[831,3607,3608,3611],{},[603,3609,3610],{},"30",[595,3612,3065],{},[595,3614,966],{},[850,3616,3617,3619],{},[603,3618,854],{},[603,3620,842],{},[613,3622,3623],{"encoding":615},"\\sin 30^\\circ = \\frac{1}{2}",[572,3625,3627,3680],{"className":3626,"ariaHidden":621},[620],[572,3628,3630,3633,3636,3639,3642,3671,3674,3677],{"className":3629},[625],[572,3631],{"className":3632,"style":3096},[629],[572,3634,593],{"className":3635},[634],[572,3637],{"className":3638,"style":743},[742],[572,3640,605],{"className":3641},[642],[572,3643,3645,3648],{"className":3644},[642],[572,3646,3107],{"className":3647},[642],[572,3649,3651],{"className":3650},[879],[572,3652,3654],{"className":3653},[883],[572,3655,3657],{"className":3656},[887],[572,3658,3660],{"className":3659,"style":3096},[891],[572,3661,3662,3665],{"style":1493},[572,3663],{"className":3664,"style":900},[899],[572,3666,3668],{"className":3667},[904,905,906,907],[572,3669,3065],{"className":3670},[1217,907],[572,3672],{"className":3673,"style":920},[742],[572,3675,966],{"className":3676},[924],[572,3678],{"className":3679,"style":920},[742],[572,3681,3683,3686],{"className":3682},[625],[572,3684],{"className":3685,"style":976},[629],[572,3687,3689,3692,3751],{"className":3688},[642],[572,3690],{"className":3691},[638,983],[572,3693,3695],{"className":3694},[850],[572,3696,3698,3743],{"className":3697},[883,990],[572,3699,3701,3740],{"className":3700},[887],[572,3702,3704,3718,3726],{"className":3703,"style":997},[891],[572,3705,3706,3709],{"style":1000},[572,3707],{"className":3708,"style":1004},[899],[572,3710,3712],{"className":3711},[904,905,906,907],[572,3713,3715],{"className":3714},[642,907],[572,3716,842],{"className":3717},[642,907],[572,3719,3720,3723],{"style":1016},[572,3721],{"className":3722,"style":1004},[899],[572,3724],{"className":3725,"style":1024},[1023],[572,3727,3728,3731],{"style":1027},[572,3729],{"className":3730,"style":1004},[899],[572,3732,3734],{"className":3733},[904,905,906,907],[572,3735,3737],{"className":3736},[642,907],[572,3738,854],{"className":3739},[642,907],[572,3741,1044],{"className":3742},[1043],[572,3744,3746],{"className":3745},[887],[572,3747,3749],{"className":3748,"style":1051},[891],[572,3750],{},[572,3752],{"className":3753},[650,983],[572,3755,3757,3788],{"className":3756},[575],[572,3758,3760],{"className":3759},[579],[581,3761,3762],{"xmlns":583},[585,3763,3764,3785],{},[588,3765,3766,3772,3774,3776,3778],{},[831,3767,3768,3770],{},[603,3769,3610],{},[595,3771,3065],{},[595,3773,966],{},[603,3775,605],{},[595,3777,3294],{},[831,3779,3780,3783],{},[603,3781,3782],{},"10",[595,3784,3065],{},[613,3786,3787],{"encoding":615},"30^\\circ = 3 \\cdot 10^\\circ",[572,3789,3791,3838,3856],{"className":3790,"ariaHidden":621},[620],[572,3792,3794,3797,3800,3829,3832,3835],{"className":3793},[625],[572,3795],{"className":3796,"style":3096},[629],[572,3798,605],{"className":3799},[642],[572,3801,3803,3806],{"className":3802},[642],[572,3804,3107],{"className":3805},[642],[572,3807,3809],{"className":3808},[879],[572,3810,3812],{"className":3811},[883],[572,3813,3815],{"className":3814},[887],[572,3816,3818],{"className":3817,"style":3096},[891],[572,3819,3820,3823],{"style":1493},[572,3821],{"className":3822,"style":900},[899],[572,3824,3826],{"className":3825},[904,905,906,907],[572,3827,3065],{"className":3828},[1217,907],[572,3830],{"className":3831,"style":920},[742],[572,3833,966],{"className":3834},[924],[572,3836],{"className":3837,"style":920},[742],[572,3839,3841,3844,3847,3850,3853],{"className":3840},[625],[572,3842],{"className":3843,"style":1986},[629],[572,3845,605],{"className":3846},[642],[572,3848],{"className":3849,"style":1213},[742],[572,3851,3294],{"className":3852},[1217],[572,3854],{"className":3855,"style":1213},[742],[572,3857,3859,3862,3865],{"className":3858},[625],[572,3860],{"className":3861,"style":3096},[629],[572,3863,854],{"className":3864},[642],[572,3866,3868,3871],{"className":3867},[642],[572,3869,3107],{"className":3870},[642],[572,3872,3874],{"className":3873},[879],[572,3875,3877],{"className":3876},[883],[572,3878,3880],{"className":3879},[887],[572,3881,3883],{"className":3882,"style":3096},[891],[572,3884,3885,3888],{"style":1493},[572,3886],{"className":3887,"style":900},[899],[572,3889,3891],{"className":3890},[904,905,906,907],[572,3892,3065],{"className":3893},[1217,907]," gilt ",[572,3896,3898,3933],{"className":3897},[575],[572,3899,3901],{"className":3900},[579],[581,3902,3903],{"xmlns":583},[585,3904,3905,3930],{},[588,3906,3907,3909,3912,3914,3916,3922,3924],{},[603,3908,605],{},[591,3910,3911],{},"s",[595,3913,1103],{},[603,3915,1542],{},[831,3917,3918,3920],{},[591,3919,3911],{},[603,3921,605],{},[595,3923,966],{},[850,3925,3926,3928],{},[603,3927,854],{},[603,3929,842],{},[613,3931,3932],{"encoding":615},"3s - 4s^3 = \\frac{1}{2}",[572,3934,3936,3957,4004],{"className":3935,"ariaHidden":621},[620],[572,3937,3939,3942,3945,3948,3951,3954],{"className":3938},[625],[572,3940],{"className":3941,"style":2641},[629],[572,3943,605],{"className":3944},[642],[572,3946,3911],{"className":3947},[642,646],[572,3949],{"className":3950,"style":1213},[742],[572,3952,1103],{"className":3953},[1217],[572,3955],{"className":3956,"style":1213},[742],[572,3958,3960,3963,3966,3995,3998,4001],{"className":3959},[625],[572,3961],{"className":3962,"style":1472},[629],[572,3964,1542],{"className":3965},[642],[572,3967,3969,3972],{"className":3968},[642],[572,3970,3911],{"className":3971},[642,646],[572,3973,3975],{"className":3974},[879],[572,3976,3978],{"className":3977},[883],[572,3979,3981],{"className":3980},[887],[572,3982,3984],{"className":3983,"style":1472},[891],[572,3985,3986,3989],{"style":1493},[572,3987],{"className":3988,"style":900},[899],[572,3990,3992],{"className":3991},[904,905,906,907],[572,3993,605],{"className":3994},[642,907],[572,3996],{"className":3997,"style":920},[742],[572,3999,966],{"className":4000},[924],[572,4002],{"className":4003,"style":920},[742],[572,4005,4007,4010],{"className":4006},[625],[572,4008],{"className":4009,"style":976},[629],[572,4011,4013,4016,4075],{"className":4012},[642],[572,4014],{"className":4015},[638,983],[572,4017,4019],{"className":4018},[850],[572,4020,4022,4067],{"className":4021},[883,990],[572,4023,4025,4064],{"className":4024},[887],[572,4026,4028,4042,4050],{"className":4027,"style":997},[891],[572,4029,4030,4033],{"style":1000},[572,4031],{"className":4032,"style":1004},[899],[572,4034,4036],{"className":4035},[904,905,906,907],[572,4037,4039],{"className":4038},[642,907],[572,4040,842],{"className":4041},[642,907],[572,4043,4044,4047],{"style":1016},[572,4045],{"className":4046,"style":1004},[899],[572,4048],{"className":4049,"style":1024},[1023],[572,4051,4052,4055],{"style":1027},[572,4053],{"className":4054,"style":1004},[899],[572,4056,4058],{"className":4057},[904,905,906,907],[572,4059,4061],{"className":4060},[642,907],[572,4062,854],{"className":4063},[642,907],[572,4065,1044],{"className":4066},[1043],[572,4068,4070],{"className":4069},[887],[572,4071,4073],{"className":4072,"style":1051},[891],[572,4074],{},[572,4076],{"className":4077},[650,983]," für ",[572,4080,4082,4108],{"className":4081},[575],[572,4083,4085],{"className":4084},[579],[581,4086,4087],{"xmlns":583},[585,4088,4089,4105],{},[588,4090,4091,4093,4095,4097,4099],{},[591,4092,3911],{},[595,4094,966],{},[591,4096,593],{},[595,4098,597],{},[831,4100,4101,4103],{},[603,4102,3782],{},[595,4104,3065],{},[613,4106,4107],{"encoding":615},"s = \\sin 10^\\circ",[572,4109,4111,4129],{"className":4110,"ariaHidden":621},[620],[572,4112,4114,4117,4120,4123,4126],{"className":4113},[625],[572,4115],{"className":4116,"style":778},[629],[572,4118,3911],{"className":4119},[642,646],[572,4121],{"className":4122,"style":920},[742],[572,4124,966],{"className":4125},[924],[572,4127],{"className":4128,"style":920},[742],[572,4130,4132,4135,4138,4141,4144],{"className":4131},[625],[572,4133],{"className":4134,"style":3096},[629],[572,4136,593],{"className":4137},[634],[572,4139],{"className":4140,"style":743},[742],[572,4142,854],{"className":4143},[642],[572,4145,4147,4150],{"className":4146},[642],[572,4148,3107],{"className":4149},[642],[572,4151,4153],{"className":4152},[879],[572,4154,4156],{"className":4155},[883],[572,4157,4159],{"className":4158},[887],[572,4160,4162],{"className":4161,"style":3096},[891],[572,4163,4164,4167],{"style":1493},[572,4165],{"className":4166,"style":900},[899],[572,4168,4170],{"className":4169},[904,905,906,907],[572,4171,3065],{"className":4172},[1217,907],". Also ist ",[572,4175,4177,4199],{"className":4176},[575],[572,4178,4180],{"className":4179},[579],[581,4181,4182],{"xmlns":583},[585,4183,4184,4196],{},[588,4185,4186,4188,4190],{},[591,4187,593],{},[595,4189,597],{},[831,4191,4192,4194],{},[603,4193,3782],{},[595,4195,3065],{},[613,4197,4198],{"encoding":615},"\\sin 10^\\circ",[572,4200,4202],{"className":4201,"ariaHidden":621},[620],[572,4203,4205,4208,4211,4214,4217],{"className":4204},[625],[572,4206],{"className":4207,"style":3096},[629],[572,4209,593],{"className":4210},[634],[572,4212],{"className":4213,"style":743},[742],[572,4215,854],{"className":4216},[642],[572,4218,4220,4223],{"className":4219},[642],[572,4221,3107],{"className":4222},[642],[572,4224,4226],{"className":4225},[879],[572,4227,4229],{"className":4228},[883],[572,4230,4232],{"className":4231},[887],[572,4233,4235],{"className":4234,"style":3096},[891],[572,4236,4237,4240],{"style":1493},[572,4238],{"className":4239,"style":900},[899],[572,4241,4243],{"className":4242},[904,905,906,907],[572,4244,3065],{"className":4245},[1217,907]," eine Nullstelle von",[572,4248,4250],{"className":4249},[1061],[572,4251,4253,4287],{"className":4252},[575],[572,4254,4256],{"className":4255},[579],[581,4257,4258],{"xmlns":583,"display":1070},[585,4259,4260,4284],{},[588,4261,4262,4264,4270,4272,4274,4276,4278,4280,4282],{},[603,4263,3301],{},[831,4265,4266,4268],{},[591,4267,3911],{},[603,4269,605],{},[595,4271,1103],{},[603,4273,3100],{},[591,4275,3911],{},[595,4277,1561],{},[603,4279,854],{},[595,4281,966],{},[603,4283,3107],{},[613,4285,4286],{"encoding":615},"8s^3 - 6s + 1 = 0",[572,4288,4290,4337,4358,4376],{"className":4289,"ariaHidden":621},[620],[572,4291,4293,4296,4299,4328,4331,4334],{"className":4292},[625],[572,4294],{"className":4295,"style":2385},[629],[572,4297,3301],{"className":4298},[642],[572,4300,4302,4305],{"className":4301},[642],[572,4303,3911],{"className":4304},[642,646],[572,4306,4308],{"className":4307},[879],[572,4309,4311],{"className":4310},[883],[572,4312,4314],{"className":4313},[887],[572,4315,4317],{"className":4316,"style":2422},[891],[572,4318,4319,4322],{"style":2425},[572,4320],{"className":4321,"style":900},[899],[572,4323,4325],{"className":4324},[904,905,906,907],[572,4326,605],{"className":4327},[642,907],[572,4329],{"className":4330,"style":1213},[742],[572,4332,1103],{"className":4333},[1217],[572,4335],{"className":4336,"style":1213},[742],[572,4338,4340,4343,4346,4349,4352,4355],{"className":4339},[625],[572,4341],{"className":4342,"style":2641},[629],[572,4344,3100],{"className":4345},[642],[572,4347,3911],{"className":4348},[642,646],[572,4350],{"className":4351,"style":1213},[742],[572,4353,1561],{"className":4354},[1217],[572,4356],{"className":4357,"style":1213},[742],[572,4359,4361,4364,4367,4370,4373],{"className":4360},[625],[572,4362],{"className":4363,"style":1986},[629],[572,4365,854],{"className":4366},[642],[572,4368],{"className":4369,"style":920},[742],[572,4371,966],{"className":4372},[924],[572,4374],{"className":4375,"style":920},[742],[572,4377,4379,4382],{"className":4378},[625],[572,4380],{"className":4381,"style":1986},[629],[572,4383,3107],{"className":4384},[642],[564,4386,4387,4388,4462,4463,1756],{},"Ist ",[572,4389,4391,4414],{"className":4390},[575],[572,4392,4394],{"className":4393},[579],[581,4395,4396],{"xmlns":583},[585,4397,4398,4411],{},[588,4399,4400,4402,4404,4406,4408],{},[591,4401,593],{},[595,4403,597],{},[591,4405,608],{},[595,4407,966],{},[603,4409,4410],{},"0,6",[613,4412,4413],{"encoding":615},"\\sin x = 0{,}6",[572,4415,4417,4441],{"className":4416,"ariaHidden":621},[620],[572,4418,4420,4423,4426,4429,4432,4435,4438],{"className":4419},[625],[572,4421],{"className":4422,"style":735},[629],[572,4424,593],{"className":4425},[634],[572,4427],{"className":4428,"style":743},[742],[572,4430,608],{"className":4431},[642,646],[572,4433],{"className":4434,"style":920},[742],[572,4436,966],{"className":4437},[924],[572,4439],{"className":4440,"style":920},[742],[572,4442,4444,4448,4451,4459],{"className":4443},[625],[572,4445],{"className":4446,"style":4447},[629],"height:0.8389em;vertical-align:-0.1944em;",[572,4449,3107],{"className":4450},[642],[572,4452,4454],{"className":4453},[642],[572,4455,4458],{"className":4456},[4457],"mpunct",",",[572,4460,3100],{"className":4461},[642],", folgt ",[572,4464,4466,4509],{"className":4465},[575],[572,4467,4469],{"className":4468},[579],[581,4470,4471],{"xmlns":583},[585,4472,4473,4506],{},[588,4474,4475,4477,4479,4481,4483,4485,4487,4489,4492,4494,4496,4498,4501,4503],{},[591,4476,593],{},[595,4478,597],{},[595,4480,601],{"stretchy":600},[603,4482,605],{},[591,4484,608],{},[595,4486,611],{"stretchy":600},[595,4488,966],{},[603,4490,4491],{},"1,8",[595,4493,1103],{},[603,4495,1542],{},[595,4497,3294],{},[603,4499,4500],{},"0,216",[595,4502,966],{},[603,4504,4505],{},"0,936",[613,4507,4508],{"encoding":615},"\\sin(3x) = 1{,}8 - 4 \\cdot 0{,}216 = 0{,}936",[572,4510,4512,4542,4569,4587,4615],{"className":4511,"ariaHidden":621},[620],[572,4513,4515,4518,4521,4524,4527,4530,4533,4536,4539],{"className":4514},[625],[572,4516],{"className":4517,"style":630},[629],[572,4519,593],{"className":4520},[634],[572,4522,601],{"className":4523},[638],[572,4525,605],{"className":4526},[642],[572,4528,608],{"className":4529},[642,646],[572,4531,611],{"className":4532},[650],[572,4534],{"className":4535,"style":920},[742],[572,4537,966],{"className":4538},[924],[572,4540],{"className":4541,"style":920},[742],[572,4543,4545,4548,4551,4557,4560,4563,4566],{"className":4544},[625],[572,4546],{"className":4547,"style":4447},[629],[572,4549,854],{"className":4550},[642],[572,4552,4554],{"className":4553},[642],[572,4555,4458],{"className":4556},[4457],[572,4558,3301],{"className":4559},[642],[572,4561],{"className":4562,"style":1213},[742],[572,4564,1103],{"className":4565},[1217],[572,4567],{"className":4568,"style":1213},[742],[572,4570,4572,4575,4578,4581,4584],{"className":4571},[625],[572,4573],{"className":4574,"style":1986},[629],[572,4576,1542],{"className":4577},[642],[572,4579],{"className":4580,"style":1213},[742],[572,4582,3294],{"className":4583},[1217],[572,4585],{"className":4586,"style":1213},[742],[572,4588,4590,4593,4596,4602,4606,4609,4612],{"className":4589},[625],[572,4591],{"className":4592,"style":4447},[629],[572,4594,3107],{"className":4595},[642],[572,4597,4599],{"className":4598},[642],[572,4600,4458],{"className":4601},[4457],[572,4603,4605],{"className":4604},[642],"216",[572,4607],{"className":4608,"style":920},[742],[572,4610,966],{"className":4611},[924],[572,4613],{"className":4614,"style":920},[742],[572,4616,4618,4621,4624,4630],{"className":4617},[625],[572,4619],{"className":4620,"style":4447},[629],[572,4622,3107],{"className":4623},[642],[572,4625,4627],{"className":4626},[642],[572,4628,4458],{"className":4629},[4457],[572,4631,4633],{"className":4632},[642],"936",[559,4635,4637],{"id":4636},"typische-fehler","Typische Fehler",[1357,4639,4640,4734,4959],{},[1360,4641,4642,4733],{},[572,4643,4645,4679],{"className":4644},[575],[572,4646,4648],{"className":4647},[579],[581,4649,4650],{"xmlns":583},[585,4651,4652,4676],{},[588,4653,4654,4656,4658,4660,4662,4664,4666,4668,4670,4672,4674],{},[591,4655,593],{},[595,4657,597],{},[595,4659,601],{"stretchy":600},[603,4661,605],{},[591,4663,608],{},[595,4665,611],{"stretchy":600},[595,4667,966],{},[603,4669,605],{},[591,4671,593],{},[595,4673,597],{},[591,4675,608],{},[613,4677,4678],{"encoding":615},"\\sin(3x) = 3\\sin x",[572,4680,4682,4712],{"className":4681,"ariaHidden":621},[620],[572,4683,4685,4688,4691,4694,4697,4700,4703,4706,4709],{"className":4684},[625],[572,4686],{"className":4687,"style":630},[629],[572,4689,593],{"className":4690},[634],[572,4692,601],{"className":4693},[638],[572,4695,605],{"className":4696},[642],[572,4698,608],{"className":4699},[642,646],[572,4701,611],{"className":4702},[650],[572,4704],{"className":4705,"style":920},[742],[572,4707,966],{"className":4708},[924],[572,4710],{"className":4711,"style":920},[742],[572,4713,4715,4718,4721,4724,4727,4730],{"className":4714},[625],[572,4716],{"className":4717,"style":735},[629],[572,4719,605],{"className":4720},[642],[572,4722],{"className":4723,"style":743},[742],[572,4725,593],{"className":4726},[634],[572,4728],{"className":4729,"style":743},[742],[572,4731,608],{"className":4732},[642,646]," setzen. Der Sinus ist nicht linear.",[1360,4735,4736,4737,4822,4823,651,4907,1756],{},"Die Vorzeichen vertauschen: Beim Sinus steht ",[572,4738,4740,4768],{"className":4739},[575],[572,4741,4743],{"className":4742},[579],[581,4744,4745],{"xmlns":583},[585,4746,4747,4765],{},[588,4748,4749,4751,4753,4763],{},[595,4750,1103],{},[603,4752,1542],{},[831,4754,4755,4761],{},[588,4756,4757,4759],{},[591,4758,593],{},[595,4760,597],{},[603,4762,605],{},[591,4764,608],{},[613,4766,4767],{"encoding":615},"-4\\sin^3 x",[572,4769,4771],{"className":4770,"ariaHidden":621},[620],[572,4772,4774,4778,4781,4784,4787,4816,4819],{"className":4773},[625],[572,4775],{"className":4776,"style":4777},[629],"height:0.9552em;vertical-align:-0.0833em;",[572,4779,1103],{"className":4780},[642],[572,4782,1542],{"className":4783},[642],[572,4785],{"className":4786,"style":743},[742],[572,4788,4790,4793],{"className":4789},[634],[572,4791,593],{"className":4792},[634],[572,4794,4796],{"className":4795},[879],[572,4797,4799],{"className":4798},[883],[572,4800,4802],{"className":4801},[887],[572,4803,4805],{"className":4804,"style":1399},[891],[572,4806,4807,4810],{"style":1420},[572,4808],{"className":4809,"style":900},[899],[572,4811,4813],{"className":4812},[904,905,906,907],[572,4814,605],{"className":4815},[642,907],[572,4817],{"className":4818,"style":743},[742],[572,4820,608],{"className":4821},[642,646],", beim Kosinus ",[572,4824,4826,4854],{"className":4825},[575],[572,4827,4829],{"className":4828},[579],[581,4830,4831],{"xmlns":583},[585,4832,4833,4851],{},[588,4834,4835,4837,4839,4849],{},[595,4836,1561],{},[603,4838,1542],{},[831,4840,4841,4847],{},[588,4842,4843,4845],{},[591,4844,666],{},[595,4846,597],{},[603,4848,605],{},[591,4850,608],{},[613,4852,4853],{"encoding":615},"+4\\cos^3 x",[572,4855,4857],{"className":4856,"ariaHidden":621},[620],[572,4858,4860,4863,4866,4869,4872,4901,4904],{"className":4859},[625],[572,4861],{"className":4862,"style":1938},[629],[572,4864,1561],{"className":4865},[642],[572,4867,1542],{"className":4868},[642],[572,4870],{"className":4871,"style":743},[742],[572,4873,4875,4878],{"className":4874},[634],[572,4876,666],{"className":4877},[634],[572,4879,4881],{"className":4880},[879],[572,4882,4884],{"className":4883},[883],[572,4885,4887],{"className":4886},[887],[572,4888,4890],{"className":4889,"style":1472},[891],[572,4891,4892,4895],{"style":1493},[572,4893],{"className":4894,"style":900},[899],[572,4896,4898],{"className":4897},[904,905,906,907],[572,4899,605],{"className":4900},[642,907],[572,4902],{"className":4903,"style":743},[742],[572,4905,608],{"className":4906},[642,646],[572,4908,4910,4932],{"className":4909},[575],[572,4911,4913],{"className":4912},[579],[581,4914,4915],{"xmlns":583},[585,4916,4917,4929],{},[588,4918,4919,4921,4923,4925,4927],{},[595,4920,1103],{},[603,4922,605],{},[591,4924,666],{},[595,4926,597],{},[591,4928,608],{},[613,4930,4931],{"encoding":615},"-3\\cos x",[572,4933,4935],{"className":4934,"ariaHidden":621},[620],[572,4936,4938,4941,4944,4947,4950,4953,4956],{"className":4937},[625],[572,4939],{"className":4940,"style":2641},[629],[572,4942,1103],{"className":4943},[642],[572,4945,605],{"className":4946},[642],[572,4948],{"className":4949,"style":743},[742],[572,4951,666],{"className":4952},[634],[572,4954],{"className":4955,"style":743},[742],[572,4957,608],{"className":4958},[642,646],[1360,4960,4961,4962,5124,5125,5209,5210,5261],{},"Die Tangensformel an Stellen mit ",[572,4963,4965,4997],{"className":4964},[575],[572,4966,4968],{"className":4967},[579],[581,4969,4970],{"xmlns":583},[585,4971,4972,4994],{},[588,4973,4974,4984,4986,4988],{},[831,4975,4976,4982],{},[588,4977,4978,4980],{},[591,4979,837],{},[595,4981,597],{},[603,4983,842],{},[591,4985,608],{},[595,4987,966],{},[850,4989,4990,4992],{},[603,4991,854],{},[603,4993,605],{},[613,4995,4996],{"encoding":615},"\\tan^2 x = \\frac{1}{3}",[572,4998,5000,5050],{"className":4999,"ariaHidden":621},[620],[572,5001,5003,5006,5035,5038,5041,5044,5047],{"className":5002},[625],[572,5004],{"className":5005,"style":892},[629],[572,5007,5009,5012],{"className":5008},[634],[572,5010,837],{"className":5011},[634],[572,5013,5015],{"className":5014},[879],[572,5016,5018],{"className":5017},[883],[572,5019,5021],{"className":5020},[887],[572,5022,5024],{"className":5023,"style":892},[891],[572,5025,5026,5029],{"style":895},[572,5027],{"className":5028,"style":900},[899],[572,5030,5032],{"className":5031},[904,905,906,907],[572,5033,842],{"className":5034},[642,907],[572,5036],{"className":5037,"style":743},[742],[572,5039,608],{"className":5040},[642,646],[572,5042],{"className":5043,"style":920},[742],[572,5045,966],{"className":5046},[924],[572,5048],{"className":5049,"style":920},[742],[572,5051,5053,5056],{"className":5052},[625],[572,5054],{"className":5055,"style":976},[629],[572,5057,5059,5062,5121],{"className":5058},[642],[572,5060],{"className":5061},[638,983],[572,5063,5065],{"className":5064},[850],[572,5066,5068,5113],{"className":5067},[883,990],[572,5069,5071,5110],{"className":5070},[887],[572,5072,5074,5088,5096],{"className":5073,"style":997},[891],[572,5075,5076,5079],{"style":1000},[572,5077],{"className":5078,"style":1004},[899],[572,5080,5082],{"className":5081},[904,905,906,907],[572,5083,5085],{"className":5084},[642,907],[572,5086,605],{"className":5087},[642,907],[572,5089,5090,5093],{"style":1016},[572,5091],{"className":5092,"style":1004},[899],[572,5094],{"className":5095,"style":1024},[1023],[572,5097,5098,5101],{"style":1027},[572,5099],{"className":5100,"style":1004},[899],[572,5102,5104],{"className":5103},[904,905,906,907],[572,5105,5107],{"className":5106},[642,907],[572,5108,854],{"className":5109},[642,907],[572,5111,1044],{"className":5112},[1043],[572,5114,5116],{"className":5115},[887],[572,5117,5119],{"className":5118,"style":1051},[891],[572,5120],{},[572,5122],{"className":5123},[650,983]," verwenden, etwa bei ",[572,5126,5128,5150],{"className":5127},[575],[572,5129,5131],{"className":5130},[579],[581,5132,5133],{"xmlns":583},[585,5134,5135,5147],{},[588,5136,5137,5139,5141],{},[591,5138,608],{},[595,5140,966],{},[831,5142,5143,5145],{},[603,5144,3610],{},[595,5146,3065],{},[613,5148,5149],{"encoding":615},"x = 30^\\circ",[572,5151,5153,5171],{"className":5152,"ariaHidden":621},[620],[572,5154,5156,5159,5162,5165,5168],{"className":5155},[625],[572,5157],{"className":5158,"style":778},[629],[572,5160,608],{"className":5161},[642,646],[572,5163],{"className":5164,"style":920},[742],[572,5166,966],{"className":5167},[924],[572,5169],{"className":5170,"style":920},[742],[572,5172,5174,5177,5180],{"className":5173},[625],[572,5175],{"className":5176,"style":3096},[629],[572,5178,605],{"className":5179},[642],[572,5181,5183,5186],{"className":5182},[642],[572,5184,3107],{"className":5185},[642],[572,5187,5189],{"className":5188},[879],[572,5190,5192],{"className":5191},[883],[572,5193,5195],{"className":5194},[887],[572,5196,5198],{"className":5197,"style":3096},[891],[572,5199,5200,5203],{"style":1493},[572,5201],{"className":5202,"style":900},[899],[572,5204,5206],{"className":5205},[904,905,906,907],[572,5207,3065],{"className":5208},[1217,907],". Dort ist ",[572,5211,5213,5237],{"className":5212},[575],[572,5214,5216],{"className":5215},[579],[581,5217,5218],{"xmlns":583},[585,5219,5220,5234],{},[588,5221,5222,5224,5226,5228,5230,5232],{},[591,5223,837],{},[595,5225,597],{},[595,5227,601],{"stretchy":600},[603,5229,605],{},[591,5231,608],{},[595,5233,611],{"stretchy":600},[613,5235,5236],{"encoding":615},"\\tan(3x)",[572,5238,5240],{"className":5239,"ariaHidden":621},[620],[572,5241,5243,5246,5249,5252,5255,5258],{"className":5242},[625],[572,5244],{"className":5245,"style":630},[629],[572,5247,837],{"className":5248},[634],[572,5250,601],{"className":5251},[638],[572,5253,605],{"className":5254},[642],[572,5256,608],{"className":5257},[642,646],[572,5259,611],{"className":5260},[650]," nicht 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