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\\alpha",[567,1112,1114,1132,1180],{"className":1113,"ariaHidden":605},[604],[567,1115,1117,1120,1123,1126,1129],{"className":1116},[609],[567,1118],{"className":1119,"style":1014},[613],[567,1121,1001],{"className":1122,"style":1018},[618,825],[567,1124],{"className":1125,"style":834},[722],[567,1127,713],{"className":1128},[838],[567,1130],{"className":1131,"style":834},[722],[567,1133,1135,1139,1142,1171,1174,1177],{"className":1134},[609],[567,1136],{"className":1137,"style":1138},[613],"height:0.7574em;vertical-align:-0.0833em;",[567,1140,619],{"className":1141},[618],[567,1143,1145,1148],{"className":1144},[618],[567,1146,626],{"className":1147},[618],[567,1149,1151],{"className":1150},[630],[567,1152,1154],{"className":1153},[634],[567,1155,1157],{"className":1156},[638],[567,1158,1160],{"className":1159,"style":614},[642],[567,1161,1162,1165],{"style":645},[567,1163],{"className":1164,"style":650},[649],[567,1166,1168],{"className":1167},[654,655,656,657],[567,1169,595],{"className":1170},[661,657],[567,1172],{"className":1173,"style":809},[722],[567,1175,704],{"className":1176},[661],[567,1178],{"className":1179,"style":809},[722],[567,1181,1183,1186],{"className":1182},[609],[567,1184],{"className":1185,"style":982},[613],[567,1187,707],{"className":1188,"style":826},[618,825],". Die Gegenkathete von ",[567,1191,1193,1206],{"className":1192},[570],[567,1194,1196],{"className":1195},[574],[576,1197,1198],{"xmlns":578},[580,1199,1200,1204],{},[583,1201,1202],{},[686,1203,707],{},[597,1205,972],{"encoding":599},[567,1207,1209],{"className":1208,"ariaHidden":605},[604],[567,1210,1212,1215],{"className":1211},[609],[567,1213],{"className":1214,"style":982},[613],[567,1216,707],{"className":1217,"style":826},[618,825]," ist gleichzeitig die Ankathete von ",[567,1220,1222,1235],{"className":1221},[570],[567,1223,1225],{"className":1224},[574],[576,1226,1227],{"xmlns":578},[580,1228,1229,1233],{},[583,1230,1231],{},[686,1232,1001],{},[597,1234,1004],{"encoding":599},[567,1236,1238],{"className":1237,"ariaHidden":605},[604],[567,1239,1241,1244],{"className":1240},[609],[567,1242],{"className":1243,"style":1014},[613],[567,1245,1001],{"className":1246,"style":1018},[618,825],". Deshalb gilt ",[567,1249,1251,1277],{"className":1250},[570],[567,1252,1254],{"className":1253},[574],[576,1255,1256],{"xmlns":578},[580,1257,1258,1274],{},[583,1259,1260,1262,1264,1266,1268,1270,1272],{},[686,1261,688],{},[593,1263,691],{},[686,1265,1001],{},[593,1267,713],{},[686,1269,716],{},[593,1271,691],{},[686,1273,707],{},[597,1275,1276],{"encoding":599},"\\sin \\beta = \\cos \\alpha",[567,1278,1280,1304],{"className":1279,"ariaHidden":605},[604],[567,1281,1283,1286,1289,1292,1295,1298,1301],{"className":1282},[609],[567,1284],{"className":1285,"style":1014},[613],[567,1287,688],{"className":1288},[767],[567,1290],{"className":1291,"style":854},[722],[567,1293,1001],{"className":1294,"style":1018},[618,825],[567,1296],{"className":1297,"style":834},[722],[567,1299,713],{"className":1300},[838],[567,1302],{"className":1303,"style":834},[722],[567,1305,1307,1310,1313,1316],{"className":1306},[609],[567,1308],{"className":1309,"style":982},[613],[567,1311,716],{"className":1312},[767],[567,1314],{"className":1315,"style":854},[722],[567,1317,707],{"className":1318,"style":826},[618,825],".",[563,1321,1322,1323,1319],{},"Die Beziehung gilt nicht nur für spitze Winkel, sondern für alle Winkel. Im Bogenmaß lautet sie ",[567,1324,1326,1370],{"className":1325},[570],[567,1327,1329],{"className":1328},[574],[576,1330,1331],{"xmlns":578},[580,1332,1333,1367],{},[583,1334,1335,1337,1339,1359,1361,1363,1365],{},[686,1336,688],{},[593,1338,691],{},[583,1340,1341,1343,1352,1354,1357],{},[593,1342,695],{"fence":605},[1344,1345,1346,1349],"mfrac",{},[686,1347,1348],{},"π",[589,1350,1351],{},"2",[593,1353,704],{},[686,1355,1356],{},"x",[593,1358,710],{"fence":605},[593,1360,713],{},[686,1362,716],{},[593,1364,691],{},[686,1366,1356],{},[597,1368,1369],{"encoding":599},"\\sin\\left(\\frac{\\pi}{2} - x\\right) = \\cos x",[567,1371,1373,1508],{"className":1372,"ariaHidden":605},[604],[567,1374,1376,1380,1383,1386,1499,1502,1505],{"className":1375},[609],[567,1377],{"className":1378,"style":1379},[613],"height:1.2em;vertical-align:-0.35em;",[567,1381,688],{"className":1382},[767],[567,1384],{"className":1385,"style":854},[722],[567,1387,1390,1400,1481,1484,1487,1490,1493],{"className":1388},[1389],"minner",[567,1391,1395],{"className":1392,"style":1394},[771,1393],"delimcenter","top:0em;",[567,1396,695],{"className":1397},[1398,1399],"delimsizing","size1",[567,1401,1403,1407,1478],{"className":1402},[618],[567,1404],{"className":1405},[771,1406],"nulldelimiter",[567,1408,1410],{"className":1409},[1344],[567,1411,1414,1469],{"className":1412},[634,1413],"vlist-t2",[567,1415,1417,1464],{"className":1416},[638],[567,1418,1421,1437,1448],{"className":1419,"style":1420},[642],"height:0.6954em;",[567,1422,1424,1428],{"style":1423},"top:-2.655em;",[567,1425],{"className":1426,"style":1427},[649],"height:3em;",[567,1429,1431],{"className":1430},[654,655,656,657],[567,1432,1434],{"className":1433},[618,657],[567,1435,1351],{"className":1436},[618,657],[567,1438,1440,1443],{"style":1439},"top:-3.23em;",[567,1441],{"className":1442,"style":1427},[649],[567,1444],{"className":1445,"style":1447},[1446],"frac-line","border-bottom-width:0.04em;",[567,1449,1451,1454],{"style":1450},"top:-3.394em;",[567,1452],{"className":1453,"style":1427},[649],[567,1455,1457],{"className":1456},[654,655,656,657],[567,1458,1460],{"className":1459},[618,657],[567,1461,1348],{"className":1462,"style":1463},[618,825,657],"margin-right:0.0359em;",[567,1465,1468],{"className":1466},[1467],"vlist-s","​",[567,1470,1472],{"className":1471},[638],[567,1473,1476],{"className":1474,"style":1475},[642],"height:0.345em;",[567,1477],{},[567,1479],{"className":1480},[830,1406],[567,1482],{"className":1483,"style":809},[722],[567,1485,704],{"className":1486},[661],[567,1488],{"className":1489,"style":809},[722],[567,1491,1356],{"className":1492},[618,825],[567,1494,1496],{"className":1495,"style":1394},[830,1393],[567,1497,710],{"className":1498},[1398,1399],[567,1500],{"className":1501,"style":834},[722],[567,1503,713],{"className":1504},[838],[567,1506],{"className":1507,"style":834},[722],[567,1509,1511,1514,1517,1520],{"className":1510},[609],[567,1512],{"className":1513,"style":982},[613],[567,1515,716],{"className":1516},[767],[567,1518],{"className":1519,"style":854},[722],[567,1521,1356],{"className":1522},[618,825],[558,1524,1526],{"id":1525},"beispiele","Beispiele",[567,1528,1530],{"className":1529},[671],[567,1531,1533,1581],{"className":1532},[570],[567,1534,1536],{"className":1535},[574],[576,1537,1538],{"xmlns":578,"display":680},[580,1539,1540,1578],{},[583,1541,1542,1544,1546,1553,1555,1557,1559,1566,1568],{},[686,1543,688],{},[593,1545,691],{},[586,1547,1548,1551],{},[589,1549,1550],{},"60",[593,1552,595],{},[593,1554,713],{},[686,1556,716],{},[593,1558,691],{},[586,1560,1561,1564],{},[589,1562,1563],{},"30",[593,1565,595],{},[593,1567,713],{},[1344,1569,1570,1576],{},[1571,1572,1573],"msqrt",{},[589,1574,1575],{},"3",[589,1577,1351],{},[597,1579,1580],{"encoding":599},"\\sin 60^\\circ = \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}",[567,1582,1584,1638,1691],{"className":1583,"ariaHidden":605},[604],[567,1585,1587,1590,1593,1596,1600,1629,1632,1635],{"className":1586},[609],[567,1588],{"className":1589,"style":793},[613],[567,1591,688],{"className":1592},[767],[567,1594],{"className":1595,"style":854},[722],[567,1597,1599],{"className":1598},[618],"6",[567,1601,1603,1606],{"className":1602},[618],[567,1604,626],{"className":1605},[618],[567,1607,1609],{"className":1608},[630],[567,1610,1612],{"className":1611},[634],[567,1613,1615],{"className":1614},[638],[567,1616,1618],{"className":1617,"style":793},[642],[567,1619,1620,1623],{"style":796},[567,1621],{"className":1622,"style":650},[649],[567,1624,1626],{"className":1625},[654,655,656,657],[567,1627,595],{"className":1628},[661,657],[567,1630],{"className":1631,"style":834},[722],[567,1633,713],{"className":1634},[838],[567,1636],{"className":1637,"style":834},[722],[567,1639,1641,1644,1647,1650,1653,1682,1685,1688],{"className":1640},[609],[567,1642],{"className":1643,"style":793},[613],[567,1645,716],{"className":1646},[767],[567,1648],{"className":1649,"style":854},[722],[567,1651,1575],{"className":1652},[618],[567,1654,1656,1659],{"className":1655},[618],[567,1657,626],{"className":1658},[618],[567,1660,1662],{"className":1661},[630],[567,1663,1665],{"className":1664},[634],[567,1666,1668],{"className":1667},[638],[567,1669,1671],{"className":1670,"style":793},[642],[567,1672,1673,1676],{"style":796},[567,1674],{"className":1675,"style":650},[649],[567,1677,1679],{"className":1678},[654,655,656,657],[567,1680,595],{"className":1681},[661,657],[567,1683],{"className":1684,"style":834},[722],[567,1686,713],{"className":1687},[838],[567,1689],{"className":1690,"style":834},[722],[567,1692,1694,1698],{"className":1693},[609],[567,1695],{"className":1696,"style":1697},[613],"height:2.2702em;vertical-align:-0.686em;",[567,1699,1701,1704,1822],{"className":1700},[618],[567,1702],{"className":1703},[771,1406],[567,1705,1707],{"className":1706},[1344],[567,1708,1710,1813],{"className":1709},[634,1413],[567,1711,1713,1810],{"className":1712},[638],[567,1714,1717,1729,1737],{"className":1715,"style":1716},[642],"height:1.5842em;",[567,1718,1720,1723],{"style":1719},"top:-2.314em;",[567,1721],{"className":1722,"style":1427},[649],[567,1724,1726],{"className":1725},[618],[567,1727,1351],{"className":1728},[618],[567,1730,1731,1734],{"style":1439},[567,1732],{"className":1733,"style":1427},[649],[567,1735],{"className":1736,"style":1447},[1446],[567,1738,1740,1743],{"style":1739},"top:-3.677em;",[567,1741],{"className":1742,"style":1427},[649],[567,1744,1746],{"className":1745},[618],[567,1747,1750],{"className":1748},[618,1749],"sqrt",[567,1751,1753,1801],{"className":1752},[634,1413],[567,1754,1756,1798],{"className":1755},[638],[567,1757,1760,1775],{"className":1758,"style":1759},[642],"height:0.9072em;",[567,1761,1765,1768],{"className":1762,"style":1764},[1763],"svg-align","top:-3em;",[567,1766],{"className":1767,"style":1427},[649],[567,1769,1772],{"className":1770,"style":1771},[618],"padding-left:0.833em;",[567,1773,1575],{"className":1774},[618],[567,1776,1778,1781],{"style":1777},"top:-2.8672em;",[567,1779],{"className":1780,"style":1427},[649],[567,1782,1786],{"className":1783,"style":1785},[1784],"hide-tail","min-width:0.853em;height:1.08em;",[1787,1788,1794],"svg",{"xmlns":1789,"width":1790,"height":1791,"viewBox":1792,"preserveAspectRatio":1793},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1795,1796],"path",{"d":1797},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[567,1799,1468],{"className":1800},[1467],[567,1802,1804],{"className":1803},[638],[567,1805,1808],{"className":1806,"style":1807},[642],"height:0.1328em;",[567,1809],{},[567,1811,1468],{"className":1812},[1467],[567,1814,1816],{"className":1815},[638],[567,1817,1820],{"className":1818,"style":1819},[642],"height:0.686em;",[567,1821],{},[567,1823],{"className":1824},[830,1406],[563,1826,1827,1828,1081,1914,1999],{},"In einem rechtwinkligen Dreieck ist ",[567,1829,1831,1854],{"className":1830},[570],[567,1832,1834],{"className":1833},[574],[576,1835,1836],{"xmlns":578},[580,1837,1838,1851],{},[583,1839,1840,1842,1844],{},[686,1841,707],{},[593,1843,713],{},[586,1845,1846,1849],{},[589,1847,1848],{},"25",[593,1850,595],{},[597,1852,1853],{"encoding":599},"\\alpha = 25^\\circ",[567,1855,1857,1875],{"className":1856,"ariaHidden":605},[604],[567,1858,1860,1863,1866,1869,1872],{"className":1859},[609],[567,1861],{"className":1862,"style":982},[613],[567,1864,707],{"className":1865,"style":826},[618,825],[567,1867],{"className":1868,"style":834},[722],[567,1870,713],{"className":1871},[838],[567,1873],{"className":1874,"style":834},[722],[567,1876,1878,1881,1884],{"className":1877},[609],[567,1879],{"className":1880,"style":614},[613],[567,1882,1351],{"className":1883},[618],[567,1885,1887,1891],{"className":1886},[618],[567,1888,1890],{"className":1889},[618],"5",[567,1892,1894],{"className":1893},[630],[567,1895,1897],{"className":1896},[634],[567,1898,1900],{"className":1899},[638],[567,1901,1903],{"className":1902,"style":614},[642],[567,1904,1905,1908],{"style":645},[567,1906],{"className":1907,"style":650},[649],[567,1909,1911],{"className":1910},[654,655,656,657],[567,1912,595],{"className":1913},[661,657],[567,1915,1917,1940],{"className":1916},[570],[567,1918,1920],{"className":1919},[574],[576,1921,1922],{"xmlns":578},[580,1923,1924,1937],{},[583,1925,1926,1928,1930],{},[686,1927,1001],{},[593,1929,713],{},[586,1931,1932,1935],{},[589,1933,1934],{},"65",[593,1936,595],{},[597,1938,1939],{"encoding":599},"\\beta = 65^\\circ",[567,1941,1943,1961],{"className":1942,"ariaHidden":605},[604],[567,1944,1946,1949,1952,1955,1958],{"className":1945},[609],[567,1947],{"className":1948,"style":1014},[613],[567,1950,1001],{"className":1951,"style":1018},[618,825],[567,1953],{"className":1954,"style":834},[722],[567,1956,713],{"className":1957},[838],[567,1959],{"className":1960,"style":834},[722],[567,1962,1964,1967,1970],{"className":1963},[609],[567,1965],{"className":1966,"style":614},[613],[567,1968,1599],{"className":1969},[618],[567,1971,1973,1976],{"className":1972},[618],[567,1974,1890],{"className":1975},[618],[567,1977,1979],{"className":1978},[630],[567,1980,1982],{"className":1981},[634],[567,1983,1985],{"className":1984},[638],[567,1986,1988],{"className":1987,"style":614},[642],[567,1989,1990,1993],{"style":645},[567,1991],{"className":1992,"style":650},[649],[567,1994,1996],{"className":1995},[654,655,656,657],[567,1997,595],{"className":1998},[661,657],". Dann gilt:",[567,2001,2003],{"className":2002},[671],[567,2004,2006,2046],{"className":2005},[570],[567,2007,2009],{"className":2008},[574],[576,2010,2011],{"xmlns":578,"display":680},[580,2012,2013,2043],{},[583,2014,2015,2017,2019,2025,2027,2029,2031,2037,2040],{},[686,2016,716],{},[593,2018,691],{},[586,2020,2021,2023],{},[589,2022,1848],{},[593,2024,595],{},[593,2026,713],{},[686,2028,688],{},[593,2030,691],{},[586,2032,2033,2035],{},[589,2034,1934],{},[593,2036,595],{},[593,2038,2039],{},"≈",[589,2041,2042],{},"0,9063",[597,2044,2045],{"encoding":599},"\\cos 25^\\circ = \\sin 65^\\circ \\approx 0{,}9063",[567,2047,2049,2102,2155],{"className":2048,"ariaHidden":605},[604],[567,2050,2052,2055,2058,2061,2064,2093,2096,2099],{"className":2051},[609],[567,2053],{"className":2054,"style":793},[613],[567,2056,716],{"className":2057},[767],[567,2059],{"className":2060,"style":854},[722],[567,2062,1351],{"className":2063},[618],[567,2065,2067,2070],{"className":2066},[618],[567,2068,1890],{"className":2069},[618],[567,2071,2073],{"className":2072},[630],[567,2074,2076],{"className":2075},[634],[567,2077,2079],{"className":2078},[638],[567,2080,2082],{"className":2081,"style":793},[642],[567,2083,2084,2087],{"style":796},[567,2085],{"className":2086,"style":650},[649],[567,2088,2090],{"className":2089},[654,655,656,657],[567,2091,595],{"className":2092},[661,657],[567,2094],{"className":2095,"style":834},[722],[567,2097,713],{"className":2098},[838],[567,2100],{"className":2101,"style":834},[722],[567,2103,2105,2108,2111,2114,2117,2146,2149,2152],{"className":2104},[609],[567,2106],{"className":2107,"style":793},[613],[567,2109,688],{"className":2110},[767],[567,2112],{"className":2113,"style":854},[722],[567,2115,1599],{"className":2116},[618],[567,2118,2120,2123],{"className":2119},[618],[567,2121,1890],{"className":2122},[618],[567,2124,2126],{"className":2125},[630],[567,2127,2129],{"className":2128},[634],[567,2130,2132],{"className":2131},[638],[567,2133,2135],{"className":2134,"style":793},[642],[567,2136,2137,2140],{"style":796},[567,2138],{"className":2139,"style":650},[649],[567,2141,2143],{"className":2142},[654,655,656,657],[567,2144,595],{"className":2145},[661,657],[567,2147],{"className":2148,"style":834},[722],[567,2150,2039],{"className":2151},[838],[567,2153],{"className":2154,"style":834},[722],[567,2156,2158,2162,2165,2173],{"className":2157},[609],[567,2159],{"className":2160,"style":2161},[613],"height:0.8389em;vertical-align:-0.1944em;",[567,2163,626],{"className":2164},[618],[567,2166,2168],{"className":2167},[618],[567,2169,2172],{"className":2170},[2171],"mpunct",",",[567,2174,2176],{"className":2175},[618],"9063",[558,2178,2180],{"id":2179},"typische-fehler","Typische Fehler",[2182,2183,2184,2450],"ul",{},[2185,2186,2187,2288,2289,2449],"li",{},[567,2188,2190,2220],{"className":2189},[570],[567,2191,2193],{"className":2192},[574],[576,2194,2195],{"xmlns":578},[580,2196,2197,2217],{},[583,2198,2199,2201,2203,2205,2211,2213,2215],{},[686,2200,688],{},[593,2202,691],{},[593,2204,695],{"stretchy":694},[586,2206,2207,2209],{},[589,2208,591],{},[593,2210,595],{},[593,2212,704],{},[686,2214,707],{},[593,2216,710],{"stretchy":694},[597,2218,2219],{"encoding":599},"\\sin(90^\\circ - \\alpha)",[567,2221,2223,2276],{"className":2222,"ariaHidden":605},[604],[567,2224,2226,2229,2232,2235,2238,2267,2270,2273],{"className":2225},[609],[567,2227],{"className":2228,"style":763},[613],[567,2230,688],{"className":2231},[767],[567,2233,695],{"className":2234},[771],[567,2236,619],{"className":2237},[618],[567,2239,2241,2244],{"className":2240},[618],[567,2242,626],{"className":2243},[618],[567,2245,2247],{"className":2246},[630],[567,2248,2250],{"className":2249},[634],[567,2251,2253],{"className":2252},[638],[567,2254,2256],{"className":2255,"style":614},[642],[567,2257,2258,2261],{"style":645},[567,2259],{"className":2260,"style":650},[649],[567,2262,2264],{"className":2263},[654,655,656,657],[567,2265,595],{"className":2266},[661,657],[567,2268],{"className":2269,"style":809},[722],[567,2271,704],{"className":2272},[661],[567,2274],{"className":2275,"style":809},[722],[567,2277,2279,2282,2285],{"className":2278},[609],[567,2280],{"className":2281,"style":763},[613],[567,2283,707],{"className":2284,"style":826},[618,825],[567,2286,710],{"className":2287},[830]," als ",[567,2290,2292,2335],{"className":2291},[570],[567,2293,2295],{"className":2294},[574],[576,2296,2297],{"xmlns":578},[580,2298,2299,2332],{},[583,2300,2301,2303,2305,2311,2313,2315,2317,2319,2321,2324,2326,2328,2330],{},[686,2302,688],{},[593,2304,691],{},[586,2306,2307,2309],{},[589,2308,591],{},[593,2310,595],{},[593,2312,704],{},[686,2314,688],{},[593,2316,691],{},[686,2318,707],{},[593,2320,713],{},[589,2322,2323],{},"1",[593,2325,704],{},[686,2327,688],{},[593,2329,691],{},[686,2331,707],{},[597,2333,2334],{"encoding":599},"\\sin 90^\\circ - \\sin \\alpha = 1 - \\sin \\alpha",[567,2336,2338,2391,2415,2434],{"className":2337,"ariaHidden":605},[604],[567,2339,2341,2344,2347,2350,2353,2382,2385,2388],{"className":2340},[609],[567,2342],{"className":2343,"style":1138},[613],[567,2345,688],{"className":2346},[767],[567,2348],{"className":2349,"style":854},[722],[567,2351,619],{"className":2352},[618],[567,2354,2356,2359],{"className":2355},[618],[567,2357,626],{"className":2358},[618],[567,2360,2362],{"className":2361},[630],[567,2363,2365],{"className":2364},[634],[567,2366,2368],{"className":2367},[638],[567,2369,2371],{"className":2370,"style":614},[642],[567,2372,2373,2376],{"style":645},[567,2374],{"className":2375,"style":650},[649],[567,2377,2379],{"className":2378},[654,655,656,657],[567,2380,595],{"className":2381},[661,657],[567,2383],{"className":2384,"style":809},[722],[567,2386,704],{"className":2387},[661],[567,2389],{"className":2390,"style":809},[722],[567,2392,2394,2397,2400,2403,2406,2409,2412],{"className":2393},[609],[567,2395],{"className":2396,"style":939},[613],[567,2398,688],{"className":2399},[767],[567,2401],{"className":2402,"style":854},[722],[567,2404,707],{"className":2405,"style":826},[618,825],[567,2407],{"className":2408,"style":834},[722],[567,2410,713],{"className":2411},[838],[567,2413],{"className":2414,"style":834},[722],[567,2416,2418,2422,2425,2428,2431],{"className":2417},[609],[567,2419],{"className":2420,"style":2421},[613],"height:0.7278em;vertical-align:-0.0833em;",[567,2423,2323],{"className":2424},[618],[567,2426],{"className":2427,"style":809},[722],[567,2429,704],{"className":2430},[661],[567,2432],{"className":2433,"style":809},[722],[567,2435,2437,2440,2443,2446],{"className":2436},[609],[567,2438],{"className":2439,"style":939},[613],[567,2441,688],{"className":2442},[767],[567,2444],{"className":2445,"style":854},[722],[567,2447,707],{"className":2448,"style":826},[618,825]," rechnen. Der Sinus lässt sich nicht auf die Klammer verteilen.",[2185,2451,2452,2453,2514,2515,2579,2580,2664,2665,2798,2799,1319],{},"Komplementwinkel (",[567,2454,2456,2473],{"className":2455},[570],[567,2457,2459],{"className":2458},[574],[576,2460,2461],{"xmlns":578},[580,2462,2463,2471],{},[583,2464,2465],{},[586,2466,2467,2469],{},[589,2468,591],{},[593,2470,595],{},[597,2472,600],{"encoding":599},[567,2474,2476],{"className":2475,"ariaHidden":605},[604],[567,2477,2479,2482,2485],{"className":2478},[609],[567,2480],{"className":2481,"style":614},[613],[567,2483,619],{"className":2484},[618],[567,2486,2488,2491],{"className":2487},[618],[567,2489,626],{"className":2490},[618],[567,2492,2494],{"className":2493},[630],[567,2495,2497],{"className":2496},[634],[567,2498,2500],{"className":2499},[638],[567,2501,2503],{"className":2502,"style":614},[642],[567,2504,2505,2508],{"style":645},[567,2506],{"className":2507,"style":650},[649],[567,2509,2511],{"className":2510},[654,655,656,657],[567,2512,595],{"className":2513},[661,657],") mit Supplementwinkel (",[567,2516,2518,2537],{"className":2517},[570],[567,2519,2521],{"className":2520},[574],[576,2522,2523],{"xmlns":578},[580,2524,2525,2534],{},[583,2526,2527],{},[586,2528,2529,2532],{},[589,2530,2531],{},"180",[593,2533,595],{},[597,2535,2536],{"encoding":599},"180^\\circ",[567,2538,2540],{"className":2539,"ariaHidden":605},[604],[567,2541,2543,2546,2550],{"className":2542},[609],[567,2544],{"className":2545,"style":614},[613],[567,2547,2549],{"className":2548},[618],"18",[567,2551,2553,2556],{"className":2552},[618],[567,2554,626],{"className":2555},[618],[567,2557,2559],{"className":2558},[630],[567,2560,2562],{"className":2561},[634],[567,2563,2565],{"className":2564},[638],[567,2566,2568],{"className":2567,"style":614},[642],[567,2569,2570,2573],{"style":645},[567,2571],{"className":2572,"style":650},[649],[567,2574,2576],{"className":2575},[654,655,656,657],[567,2577,595],{"className":2578},[661,657],") verwechseln. Für ",[567,2581,2583,2605],{"className":2582},[570],[567,2584,2586],{"className":2585},[574],[576,2587,2588],{"xmlns":578},[580,2589,2590,2602],{},[583,2591,2592,2598,2600],{},[586,2593,2594,2596],{},[589,2595,2531],{},[593,2597,595],{},[593,2599,704],{},[686,2601,707],{},[597,2603,2604],{"encoding":599},"180^\\circ - \\alpha",[567,2606,2608,2655],{"className":2607,"ariaHidden":605},[604],[567,2609,2611,2614,2617,2646,2649,2652],{"className":2610},[609],[567,2612],{"className":2613,"style":1138},[613],[567,2615,2549],{"className":2616},[618],[567,2618,2620,2623],{"className":2619},[618],[567,2621,626],{"className":2622},[618],[567,2624,2626],{"className":2625},[630],[567,2627,2629],{"className":2628},[634],[567,2630,2632],{"className":2631},[638],[567,2633,2635],{"className":2634,"style":614},[642],[567,2636,2637,2640],{"style":645},[567,2638],{"className":2639,"style":650},[649],[567,2641,2643],{"className":2642},[654,655,656,657],[567,2644,595],{"className":2645},[661,657],[567,2647],{"className":2648,"style":809},[722],[567,2650,704],{"className":2651},[661],[567,2653],{"className":2654,"style":809},[722],[567,2656,2658,2661],{"className":2657},[609],[567,2659],{"className":2660,"style":982},[613],[567,2662,707],{"className":2663,"style":826},[618,825]," gilt ",[567,2666,2668,2706],{"className":2667},[570],[567,2669,2671],{"className":2670},[574],[576,2672,2673],{"xmlns":578},[580,2674,2675,2703],{},[583,2676,2677,2679,2681,2683,2689,2691,2693,2695,2697,2699,2701],{},[686,2678,688],{},[593,2680,691],{},[593,2682,695],{"stretchy":694},[586,2684,2685,2687],{},[589,2686,2531],{},[593,2688,595],{},[593,2690,704],{},[686,2692,707],{},[593,2694,710],{"stretchy":694},[593,2696,713],{},[686,2698,688],{},[593,2700,691],{},[686,2702,707],{},[597,2704,2705],{"encoding":599},"\\sin(180^\\circ - \\alpha) = \\sin \\alpha",[567,2707,2709,2762,2783],{"className":2708,"ariaHidden":605},[604],[567,2710,2712,2715,2718,2721,2724,2753,2756,2759],{"className":2711},[609],[567,2713],{"className":2714,"style":763},[613],[567,2716,688],{"className":2717},[767],[567,2719,695],{"className":2720},[771],[567,2722,2549],{"className":2723},[618],[567,2725,2727,2730],{"className":2726},[618],[567,2728,626],{"className":2729},[618],[567,2731,2733],{"className":2732},[630],[567,2734,2736],{"className":2735},[634],[567,2737,2739],{"className":2738},[638],[567,2740,2742],{"className":2741,"style":614},[642],[567,2743,2744,2747],{"style":645},[567,2745],{"className":2746,"style":650},[649],[567,2748,2750],{"className":2749},[654,655,656,657],[567,2751,595],{"className":2752},[661,657],[567,2754],{"className":2755,"style":809},[722],[567,2757,704],{"className":2758},[661],[567,2760],{"className":2761,"style":809},[722],[567,2763,2765,2768,2771,2774,2777,2780],{"className":2764},[609],[567,2766],{"className":2767,"style":763},[613],[567,2769,707],{"className":2770,"style":826},[618,825],[567,2772,710],{"className":2773},[830],[567,2775],{"className":2776,"style":834},[722],[567,2778,713],{"className":2779},[838],[567,2781],{"className":2782,"style":834},[722],[567,2784,2786,2789,2792,2795],{"className":2785},[609],[567,2787],{"className":2788,"style":939},[613],[567,2790,688],{"className":2791},[767],[567,2793],{"className":2794,"style":854},[722],[567,2796,707],{"className":2797,"style":826},[618,825],", nicht ",[567,2800,2802,2820],{"className":2801},[570],[567,2803,2805],{"className":2804},[574],[576,2806,2807],{"xmlns":578},[580,2808,2809,2817],{},[583,2810,2811,2813,2815],{},[686,2812,716],{},[593,2814,691],{},[686,2816,707],{},[597,2818,2819],{"encoding":599},"\\cos \\alpha",[567,2821,2823],{"className":2822,"ariaHidden":605},[604],[567,2824,2826,2829,2832,2835],{"className":2825},[609],[567,2827],{"className":2828,"style":982},[613],[567,2830,716],{"className":2831},[767],[567,2833],{"className":2834,"style":854},[722],[567,2836,707],{"className":2837,"style":826},[618,825],{"title":2839,"searchDepth":2840,"depth":2840,"links":2841},"",2,[2842,2843,2844],{"id":560,"depth":2840,"text":561},{"id":1525,"depth":2840,"text":1526},{"id":2179,"depth":2840,"text":2180},[2846,2849,2852,2855,2857,2860,2862],{"lhs":2847,"rhs":2848},"sin(pi\u002F2 - x)","cos(x)",{"lhs":2850,"rhs":2851},"cos(pi\u002F2 - x)","sin(x)",{"lhs":2853,"rhs":2854},"sin(60*pi\u002F180)","cos(30*pi\u002F180)",{"lhs":2854,"rhs":2856},"sqrt(3)\u002F2",{"lhs":2858,"rhs":2859},"round(cos(25*pi\u002F180), 4)","0.9063",{"lhs":2861,"rhs":2859},"round(sin(65*pi\u002F180), 4)",{"lhs":2863,"rhs":2851},"sin(pi - x)",null,"md",{"caption":2867,"x":2868,"y":2871,"unit":2873,"items":2874},"Rechtwinkliges Dreieck mit den spitzen Winkeln α und β = 90° − α: die markierte Kathete ist Gegenkathete von α und Ankathete von β",[2869,2870],-0.6,5,[2869,2872],3.6,48,[2875,2886,2890,2895,2900,2904],{"type":2876,"points":2877,"fill":2884,"style":2885},"polygon",[2878,2880,2882],[2879,2879],0,[2881,2879],4,[2881,2883],3,true,"muted",{"type":2887,"from":2888,"to":2889},"segment",[2881,2879],[2881,2883],{"type":2891,"at":2892,"from":2893,"to":2894},"rightAngle",[2881,2879],[2879,2879],[2881,2883],{"type":2896,"at":2897,"from":2898,"to":2899,"label":707},"angle",[2879,2879],[2881,2879],[2881,2883],{"type":2896,"at":2901,"from":2902,"to":2903,"label":1001},[2881,2883],[2879,2879],[2881,2879],{"type":2905,"at":2906,"text":2909},"label",[2907,2908],1.25,2.6,"β = 90° − α","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 268.8 201.6\" width=\"268.8\" height=\"201.6\" role=\"img\" aria-label=\"Rechtwinkliges Dreieck mit den spitzen Winkeln α und β = 90° − α: die markierte Kathete ist Gegenkathete von α und Ankathete von β\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-complementary-angles-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-complementary-angles-clip\">\u003Crect x=\"0\" y=\"0\" width=\"268.8\" height=\"201.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,172.8 220.8,172.8 220.8,28.8\" class=\"fig-muted fig-fill\"\u002F>\u003Cline x1=\"220.8\" y1=\"172.8\" x2=\"220.8\" y2=\"28.8\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 208.8 172.8 L 208.8 160.8 L 220.8 160.8\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"214.8\" cy=\"166.8\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Cpath d=\"M 28.8 172.8 L 50.8 172.8 A 22 22 0 0 0 46.4 159.6 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"61.06\" y=\"162.05\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Cpath d=\"M 220.8 28.8 L 203.2 42 A 22 22 0 0 0 220.8 50.8 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"205.59\" y=\"59.21\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">β\u003C\u002Ftext>\u003Ctext x=\"88.8\" y=\"48\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">β = 90° − α\u003C\u002Ftext>\u003C\u002Fsvg>","complementary-angles","\\sin(90^\\circ - \\alpha) = \\cos \\alpha","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sin(90^\\circ - \\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\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:0.7241em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-und-kosinus-komplementwinkel",[],[2919,2920,2921],"sine-right-triangle","cosine-right-triangle","pythagorean-identity",{"title":548,"description":2839},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-und-kosinus-komplementwinkel","Der Sinus des Komplementwinkels 90° − α ist gleich dem Kosinus von α, und umgekehrt.",[2926,2927,2928,2929],"sinus","kosinus","komplementwinkel","rechtwinkliges dreieck",[2931],{"symbol":972,"meaning":2932,"symbolHtml":2933},"Winkel (hier im Gradmaß angegeben)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","eaUe2Oq-cW_9W9cmKkoDjuOi6XsbM_Lm7cmPwXGfpAo",[2936,2939,2942],{"stem":2937,"title":2938,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fkosinus-im-rechtwinkligen-dreieck","Kosinus im rechtwinkligen Dreieck",{"stem":2940,"title":2941,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fsinus-im-rechtwinkligen-dreieck","Sinus im rechtwinkligen Dreieck",{"stem":2943,"title":2944,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftrigonometrischer-pythagoras","Trigonometrischer Pythagoras",1793824262987]