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Tangens kann jede positive Zahl annehmen, auch Werte über ",[574,1043,1045,1059],{"className":1044},[577],[574,1046,1048],{"className":1047},[581],[583,1049,1050],{"xmlns":585},[587,1051,1052,1057],{},[590,1053,1054],{},[660,1055,1056],{},"1",[597,1058,1056],{"encoding":599},[574,1060,1062],{"className":1061,"ariaHidden":605},[604],[574,1063,1065,1069],{"className":1064},[609],[574,1066],{"className":1067,"style":1068},[613],"height:0.6444em;",[574,1070,1056],{"className":1071},[618],". Er beschreibt eine ",[569,1074,1075],{},"Steigung",": Höhenunterschied geteilt durch waagerechte Strecke.",[565,1078,1079],{},"Umgestellt:",[574,1081,1084],{"className":1082},[1083],"katex-display",[574,1085,1087,1135],{"className":1086},[577],[574,1088,1090],{"className":1089},[581],[583,1091,1093],{"xmlns":585,"display":1092},"block",[587,1094,1095,1132],{},[590,1096,1097,1100,1102,1104,1107,1109,1111,1113,1116,1118,1120],{},[1098,1099,628],"mtext",{},[653,1101,655],{},[1098,1103,632],{},[653,1105,1106],{},"⋅",[593,1108,763],{},[653,1110,766],{},[593,1112,595],{},[686,1114],{"width":1115},"2em",[1098,1117,632],{},[653,1119,655],{},[772,1121,1122,1124],{},[1098,1123,628],{},[590,1125,1126,1128,1130],{},[593,1127,763],{},[653,1129,766],{},[593,1131,595],{},[597,1133,1134],{"encoding":599},"\\text{Gegenkathete} = \\text{Ankathete} \\cdot \\tan \\alpha\n\\qquad\n\\text{Ankathete} = \\frac{\\text{Gegenkathete}}{\\tan \\alpha}",[574,1136,1138,1160,1183,1217],{"className":1137,"ariaHidden":605},[604],[574,1139,1141,1144,1151,1154,1157],{"className":1140},[609],[574,1142],{"className":1143,"style":942},[613],[574,1145,1148],{"className":1146},[618,1147],"text",[574,1149,628],{"className":1150},[618],[574,1152],{"className":1153,"style":687},[686],[574,1155,655],{"className":1156},[691],[574,1158],{"className":1159,"style":687},[686],[574,1161,1163,1167,1173,1177,1180],{"className":1162},[609],[574,1164],{"className":1165,"style":1166},[613],"height:0.6944em;",[574,1168,1170],{"className":1169},[618,1147],[574,1171,632],{"className":1172},[618],[574,1174],{"className":1175,"style":1176},[686],"margin-right:0.2222em;",[574,1178,1106],{"className":1179},[747],[574,1181],{"className":1182,"style":1176},[686],[574,1184,1186,1189,1192,1195,1198,1202,1208,1211,1214],{"className":1185},[609],[574,1187],{"className":1188,"style":1166},[613],[574,1190,763],{"className":1191},[796],[574,1193],{"className":1194,"style":800},[686],[574,1196,595],{"className":1197,"style":620},[618,619],[574,1199],{"className":1200,"style":1201},[686],"margin-right:2em;",[574,1203,1205],{"className":1204},[618,1147],[574,1206,632],{"className":1207},[618],[574,1209],{"className":1210,"style":687},[686],[574,1212,655],{"className":1213},[691],[574,1215],{"className":1216,"style":687},[686],[574,1218,1220,1224],{"className":1219},[609],[574,1221],{"className":1222,"style":1223},[613],"height:2.0574em;vertical-align:-0.686em;",[574,1225,1227,1230,1296],{"className":1226},[618],[574,1228],{"className":1229},[826,827],[574,1231,1233],{"className":1232},[772],[574,1234,1236,1287],{"className":1235},[720,834],[574,1237,1239,1284],{"className":1238},[724],[574,1240,1243,1261,1269],{"className":1241,"style":1242},[728],"height:1.3714em;",[574,1244,1246,1249],{"style":1245},"top:-2.314em;",[574,1247],{"className":1248,"style":848},[735],[574,1250,1252,1255,1258],{"className":1251},[618],[574,1253,763],{"className":1254},[796],[574,1256],{"className":1257,"style":800},[686],[574,1259,595],{"className":1260,"style":620},[618,619],[574,1262,1263,1266],{"style":860},[574,1264],{"className":1265,"style":848},[735],[574,1267],{"className":1268,"style":868},[867],[574,1270,1272,1275],{"style":1271},"top:-3.677em;",[574,1273],{"className":1274,"style":848},[735],[574,1276,1278],{"className":1277},[618],[574,1279,1281],{"className":1280},[618,1147],[574,1282,628],{"className":1283},[618],[574,1285,888],{"className":1286},[887],[574,1288,1290],{"className":1289},[724],[574,1291,1294],{"className":1292,"style":1293},[728],"height:0.686em;",[574,1295],{},[574,1297],{"className":1298},[901,827],[560,1300,1302],{"id":1301},"beispiele","Beispiele",[565,1304,1305,1306,1393],{},"Bei ",[574,1307,1309,1332],{"className":1308},[577],[574,1310,1312],{"className":1311},[581],[583,1313,1314],{"xmlns":585},[587,1315,1316,1329],{},[590,1317,1318,1320,1322],{},[593,1319,595],{},[653,1321,655],{},[657,1323,1324,1327],{},[660,1325,1326],{},"45",[653,1328,665],{},[597,1330,1331],{"encoding":599},"\\alpha = 45^\\circ",[574,1333,1335,1353],{"className":1334,"ariaHidden":605},[604],[574,1336,1338,1341,1344,1347,1350],{"className":1337},[609],[574,1339],{"className":1340,"style":614},[613],[574,1342,595],{"className":1343,"style":620},[618,619],[574,1345],{"className":1346,"style":687},[686],[574,1348,655],{"className":1349},[691],[574,1351],{"className":1352,"style":687},[686],[574,1354,1356,1359,1363],{"className":1355},[609],[574,1357],{"className":1358,"style":701},[613],[574,1360,1362],{"className":1361},[618],"4",[574,1364,1366,1370],{"className":1365},[618],[574,1367,1369],{"className":1368},[618],"5",[574,1371,1373],{"className":1372},[716],[574,1374,1376],{"className":1375},[720],[574,1377,1379],{"className":1378},[724],[574,1380,1382],{"className":1381,"style":701},[728],[574,1383,1384,1387],{"style":731},[574,1385],{"className":1386,"style":736},[735],[574,1388,1390],{"className":1389},[740,741,742,743],[574,1391,665],{"className":1392},[747,743]," sind beide Katheten gleich lang:",[574,1395,1397],{"className":1396},[1083],[574,1398,1400,1426],{"className":1399},[577],[574,1401,1403],{"className":1402},[581],[583,1404,1405],{"xmlns":585,"display":1092},[587,1406,1407,1423],{},[590,1408,1409,1411,1413,1419,1421],{},[593,1410,763],{},[653,1412,766],{},[657,1414,1415,1417],{},[660,1416,1326],{},[653,1418,665],{},[653,1420,655],{},[660,1422,1056],{},[597,1424,1425],{"encoding":599},"\\tan 45^\\circ = 1",[574,1427,1429,1484],{"className":1428,"ariaHidden":605},[604],[574,1430,1432,1436,1439,1442,1445,1475,1478,1481],{"className":1431},[609],[574,1433],{"className":1434,"style":1435},[613],"height:0.7241em;",[574,1437,763],{"className":1438},[796],[574,1440],{"className":1441,"style":800},[686],[574,1443,1362],{"className":1444},[618],[574,1446,1448,1451],{"className":1447},[618],[574,1449,1369],{"className":1450},[618],[574,1452,1454],{"className":1453},[716],[574,1455,1457],{"className":1456},[720],[574,1458,1460],{"className":1459},[724],[574,1461,1463],{"className":1462,"style":1435},[728],[574,1464,1466,1469],{"style":1465},"top:-3.113em;margin-right:0.05em;",[574,1467],{"className":1468,"style":736},[735],[574,1470,1472],{"className":1471},[740,741,742,743],[574,1473,665],{"className":1474},[747,743],[574,1476],{"className":1477,"style":687},[686],[574,1479,655],{"className":1480},[691],[574,1482],{"className":1483,"style":687},[686],[574,1485,1487,1490],{"className":1486},[609],[574,1488],{"className":1489,"style":1068},[613],[574,1491,1056],{"className":1492},[618],[565,1494,1495,1496,1541,1542,1606],{},"Man steht ",[574,1497,1499,1520],{"className":1498},[577],[574,1500,1502],{"className":1501},[581],[583,1503,1504],{"xmlns":585},[587,1505,1506,1517],{},[590,1507,1508,1511,1514],{},[660,1509,1510],{},"20",[1098,1512,1513],{}," ",[1098,1515,1516],{},"m",[597,1518,1519],{"encoding":599},"20\\,\\text{m}",[574,1521,1523],{"className":1522,"ariaHidden":605},[604],[574,1524,1526,1529,1532,1535],{"className":1525},[609],[574,1527],{"className":1528,"style":1068},[613],[574,1530,1510],{"className":1531},[618],[574,1533],{"className":1534,"style":800},[686],[574,1536,1538],{"className":1537},[618,1147],[574,1539,1516],{"className":1540},[618]," von einem Baum entfernt und sieht die Spitze unter einem Winkel von ",[574,1543,1545,1564],{"className":1544},[577],[574,1546,1548],{"className":1547},[581],[583,1549,1550],{"xmlns":585},[587,1551,1552,1561],{},[590,1553,1554],{},[657,1555,1556,1559],{},[660,1557,1558],{},"35",[653,1560,665],{},[597,1562,1563],{"encoding":599},"35^\\circ",[574,1565,1567],{"className":1566,"ariaHidden":605},[604],[574,1568,1570,1573,1577],{"className":1569},[609],[574,1571],{"className":1572,"style":701},[613],[574,1574,1576],{"className":1575},[618],"3",[574,1578,1580,1583],{"className":1579},[618],[574,1581,1369],{"className":1582},[618],[574,1584,1586],{"className":1585},[716],[574,1587,1589],{"className":1588},[720],[574,1590,1592],{"className":1591},[724],[574,1593,1595],{"className":1594,"style":701},[728],[574,1596,1597,1600],{"style":731},[574,1598],{"className":1599,"style":736},[735],[574,1601,1603],{"className":1602},[740,741,742,743],[574,1604,665],{"className":1605},[747,743],". Die Augenhöhe wird vernachlässigt, man denkt sich den Blick also vom Boden aus. Die Entfernung ist die Ankathete, die Baumhöhe die Gegenkathete:",[574,1608,1610],{"className":1609},[1083],[574,1611,1613,1658],{"className":1612},[577],[574,1614,1616],{"className":1615},[581],[583,1617,1618],{"xmlns":585,"display":1092},[587,1619,1620,1655],{},[590,1621,1622,1625,1627,1629,1631,1633,1635,1637,1639,1645,1648,1651,1653],{},[593,1623,1624],{},"h",[653,1626,655],{},[660,1628,1510],{},[1098,1630,1513],{},[1098,1632,1516],{},[653,1634,1106],{},[593,1636,763],{},[653,1638,766],{},[657,1640,1641,1643],{},[660,1642,1558],{},[653,1644,665],{},[653,1646,1647],{},"≈",[660,1649,1650],{},"14,0",[1098,1652,1513],{},[1098,1654,1516],{},[597,1656,1657],{"encoding":599},"h = 20\\,\\text{m} \\cdot \\tan 35^\\circ \\approx 14{,}0\\,\\text{m}",[574,1659,1661,1679,1706,1759],{"className":1660,"ariaHidden":605},[604],[574,1662,1664,1667,1670,1673,1676],{"className":1663},[609],[574,1665],{"className":1666,"style":1166},[613],[574,1668,1624],{"className":1669},[618,619],[574,1671],{"className":1672,"style":687},[686],[574,1674,655],{"className":1675},[691],[574,1677],{"className":1678,"style":687},[686],[574,1680,1682,1685,1688,1691,1697,1700,1703],{"className":1681},[609],[574,1683],{"className":1684,"style":1068},[613],[574,1686,1510],{"className":1687},[618],[574,1689],{"className":1690,"style":800},[686],[574,1692,1694],{"className":1693},[618,1147],[574,1695,1516],{"className":1696},[618],[574,1698],{"className":1699,"style":1176},[686],[574,1701,1106],{"className":1702},[747],[574,1704],{"className":1705,"style":1176},[686],[574,1707,1709,1712,1715,1718,1721,1750,1753,1756],{"className":1708},[609],[574,1710],{"className":1711,"style":1435},[613],[574,1713,763],{"className":1714},[796],[574,1716],{"className":1717,"style":800},[686],[574,1719,1576],{"className":1720},[618],[574,1722,1724,1727],{"className":1723},[618],[574,1725,1369],{"className":1726},[618],[574,1728,1730],{"className":1729},[716],[574,1731,1733],{"className":1732},[720],[574,1734,1736],{"className":1735},[724],[574,1737,1739],{"className":1738,"style":1435},[728],[574,1740,1741,1744],{"style":1465},[574,1742],{"className":1743,"style":736},[735],[574,1745,1747],{"className":1746},[740,741,742,743],[574,1748,665],{"className":1749},[747,743],[574,1751],{"className":1752,"style":687},[686],[574,1754,1647],{"className":1755},[691],[574,1757],{"className":1758,"style":687},[686],[574,1760,1762,1766,1770,1778,1781,1784],{"className":1761},[609],[574,1763],{"className":1764,"style":1765},[613],"height:0.8389em;vertical-align:-0.1944em;",[574,1767,1769],{"className":1768},[618],"14",[574,1771,1773],{"className":1772},[618],[574,1774,1777],{"className":1775},[1776],"mpunct",",",[574,1779,712],{"className":1780},[618],[574,1782],{"className":1783,"style":800},[686],[574,1785,1787],{"className":1786},[618,1147],[574,1788,1516],{"className":1789},[618],[565,1791,1792,1793,1836,1837,1890],{},"Eine Rampe steigt auf ",[574,1794,1796,1815],{"className":1795},[577],[574,1797,1799],{"className":1798},[581],[583,1800,1801],{"xmlns":585},[587,1802,1803,1812],{},[590,1804,1805,1808,1810],{},[660,1806,1807],{},"10",[1098,1809,1513],{},[1098,1811,1516],{},[597,1813,1814],{"encoding":599},"10\\,\\text{m}",[574,1816,1818],{"className":1817,"ariaHidden":605},[604],[574,1819,1821,1824,1827,1830],{"className":1820},[609],[574,1822],{"className":1823,"style":1068},[613],[574,1825,1807],{"className":1826},[618],[574,1828],{"className":1829,"style":800},[686],[574,1831,1833],{"className":1832},[618,1147],[574,1834,1516],{"className":1835},[618]," waagerechter Strecke um ",[574,1838,1840,1859],{"className":1839},[577],[574,1841,1843],{"className":1842},[581],[583,1844,1845],{"xmlns":585},[587,1846,1847,1856],{},[590,1848,1849,1852,1854],{},[660,1850,1851],{},"1,2",[1098,1853,1513],{},[1098,1855,1516],{},[597,1857,1858],{"encoding":599},"1{,}2\\,\\text{m}",[574,1860,1862],{"className":1861,"ariaHidden":605},[604],[574,1863,1865,1868,1871,1877,1881,1884],{"className":1864},[609],[574,1866],{"className":1867,"style":1765},[613],[574,1869,1056],{"className":1870},[618],[574,1872,1874],{"className":1873},[618],[574,1875,1777],{"className":1876},[1776],[574,1878,1880],{"className":1879},[618],"2",[574,1882],{"className":1883,"style":800},[686],[574,1885,1887],{"className":1886},[618,1147],[574,1888,1516],{"className":1889},[618]," an. Ihr Steigungswinkel:",[574,1892,1894],{"className":1893},[1083],[574,1895,1897,1973],{"className":1896},[577],[574,1898,1900],{"className":1899},[581],[583,1901,1902],{"xmlns":585,"display":1092},[587,1903,1904,1970],{},[590,1905,1906,1908,1910,1912,1914,1920,1922,1925,1928,1931,1933,1935,1937,1952,1956,1958,1961,1963],{},[593,1907,763],{},[653,1909,766],{},[593,1911,595],{},[653,1913,655],{},[772,1915,1916,1918],{},[660,1917,1851],{},[660,1919,1807],{},[653,1921,655],{},[660,1923,1924],{},"0,12",[686,1926],{"width":1927},"1em",[653,1929,1930],{},"⇒",[686,1932],{"width":1927},[593,1934,595],{},[653,1936,655],{},[657,1938,1939,1945],{},[590,1940,1941,1943],{},[593,1942,763],{},[653,1944,766],{},[590,1946,1947,1950],{},[653,1948,1949],{},"−",[660,1951,1056],{},[653,1953,1955],{"stretchy":1954},"false","(",[660,1957,1924],{},[653,1959,1960],{"stretchy":1954},")",[653,1962,1647],{},[657,1964,1965,1968],{},[660,1966,1967],{},"6,84",[653,1969,665],{},[597,1971,1972],{"encoding":599},"\\tan \\alpha = \\frac{1{,}2}{10} = 0{,}12\n\\quad\\Rightarrow\\quad\n\\alpha = \\tan^{-1}(0{,}12) \\approx 6{,}84^\\circ",[574,1974,1976,2000,2088,2123,2141,2211],{"className":1975,"ariaHidden":605},[604],[574,1977,1979,1982,1985,1988,1991,1994,1997],{"className":1978},[609],[574,1980],{"className":1981,"style":792},[613],[574,1983,763],{"className":1984},[796],[574,1986],{"className":1987,"style":800},[686],[574,1989,595],{"className":1990,"style":620},[618,619],[574,1992],{"className":1993,"style":687},[686],[574,1995,655],{"className":1996},[691],[574,1998],{"className":1999,"style":687},[686],[574,2001,2003,2007,2079,2082,2085],{"className":2002},[609],[574,2004],{"className":2005,"style":2006},[613],"height:2.0074em;vertical-align:-0.686em;",[574,2008,2010,2013,2076],{"className":2009},[618],[574,2011],{"className":2012},[826,827],[574,2014,2016],{"className":2015},[772],[574,2017,2019,2068],{"className":2018},[720,834],[574,2020,2022,2065],{"className":2021},[724],[574,2023,2026,2037,2045],{"className":2024,"style":2025},[728],"height:1.3214em;",[574,2027,2028,2031],{"style":1245},[574,2029],{"className":2030,"style":848},[735],[574,2032,2034],{"className":2033},[618],[574,2035,1807],{"className":2036},[618],[574,2038,2039,2042],{"style":860},[574,2040],{"className":2041,"style":848},[735],[574,2043],{"className":2044,"style":868},[867],[574,2046,2047,2050],{"style":1271},[574,2048],{"className":2049,"style":848},[735],[574,2051,2053,2056,2062],{"className":2052},[618],[574,2054,1056],{"className":2055},[618],[574,2057,2059],{"className":2058},[618],[574,2060,1777],{"className":2061},[1776],[574,2063,1880],{"className":2064},[618],[574,2066,888],{"className":2067},[887],[574,2069,2071],{"className":2070},[724],[574,2072,2074],{"className":2073,"style":1293},[728],[574,2075],{},[574,2077],{"className":2078},[901,827],[574,2080],{"className":2081,"style":687},[686],[574,2083,655],{"className":2084},[691],[574,2086],{"className":2087,"style":687},[686],[574,2089,2091,2094,2097,2103,2107,2111,2114,2117,2120],{"className":2090},[609],[574,2092],{"className":2093,"style":1765},[613],[574,2095,712],{"className":2096},[618],[574,2098,2100],{"className":2099},[618],[574,2101,1777],{"className":2102},[1776],[574,2104,2106],{"className":2105},[618],"12",[574,2108],{"className":2109,"style":2110},[686],"margin-right:1em;",[574,2112],{"className":2113,"style":687},[686],[574,2115,1930],{"className":2116},[691],[574,2118],{"className":2119,"style":2110},[686],[574,2121],{"className":2122,"style":687},[686],[574,2124,2126,2129,2132,2135,2138],{"className":2125},[609],[574,2127],{"className":2128,"style":614},[613],[574,2130,595],{"className":2131,"style":620},[618,619],[574,2133],{"className":2134,"style":687},[686],[574,2136,655],{"className":2137},[691],[574,2139],{"className":2140,"style":687},[686],[574,2142,2144,2148,2184,2187,2190,2196,2199,2202,2205,2208],{"className":2143},[609],[574,2145],{"className":2146,"style":2147},[613],"height:1.1141em;vertical-align:-0.25em;",[574,2149,2151,2154],{"className":2150},[796],[574,2152,763],{"className":2153},[796],[574,2155,2157],{"className":2156},[716],[574,2158,2160],{"className":2159},[720],[574,2161,2163],{"className":2162},[724],[574,2164,2167],{"className":2165,"style":2166},[728],"height:0.8641em;",[574,2168,2169,2172],{"style":1465},[574,2170],{"className":2171,"style":736},[735],[574,2173,2175],{"className":2174},[740,741,742,743],[574,2176,2178,2181],{"className":2177},[618,743],[574,2179,1949],{"className":2180},[618,743],[574,2182,1056],{"className":2183},[618,743],[574,2185,1955],{"className":2186},[826],[574,2188,712],{"className":2189},[618],[574,2191,2193],{"className":2192},[618],[574,2194,1777],{"className":2195},[1776],[574,2197,2106],{"className":2198},[618],[574,2200,1960],{"className":2201},[901],[574,2203],{"className":2204,"style":687},[686],[574,2206,1647],{"className":2207},[691],[574,2209],{"className":2210,"style":687},[686],[574,2212,2214,2218,2222,2228,2232],{"className":2213},[609],[574,2215],{"className":2216,"style":2217},[613],"height:0.9186em;vertical-align:-0.1944em;",[574,2219,2221],{"className":2220},[618],"6",[574,2223,2225],{"className":2224},[618],[574,2226,1777],{"className":2227},[1776],[574,2229,2231],{"className":2230},[618],"8",[574,2233,2235,2238],{"className":2234},[618],[574,2236,1362],{"className":2237},[618],[574,2239,2241],{"className":2240},[716],[574,2242,2244],{"className":2243},[720],[574,2245,2247],{"className":2246},[724],[574,2248,2250],{"className":2249,"style":1435},[728],[574,2251,2252,2255],{"style":1465},[574,2253],{"className":2254,"style":736},[735],[574,2256,2258],{"className":2257},[740,741,742,743],[574,2259,665],{"className":2260},[747,743],[560,2262,2264],{"id":2263},"typische-fehler","Typische Fehler",[2266,2267,2268,2543,2724,2999],"ul",{},[2269,2270,2271,2272,2378,2379,2418,2419,1038],"li",{},"Bruch umgedreht: ",[574,2273,2275,2293],{"className":2274},[577],[574,2276,2278],{"className":2277},[581],[583,2279,2280],{"xmlns":585},[587,2281,2282,2290],{},[590,2283,2284],{},[772,2285,2286,2288],{},[1098,2287,632],{},[1098,2289,628],{},[597,2291,2292],{"encoding":599},"\\frac{\\text{Ankathete}}{\\text{Gegenkathete}}",[574,2294,2296],{"className":2295,"ariaHidden":605},[604],[574,2297,2299,2303],{"className":2298},[609],[574,2300],{"className":2301,"style":2302},[613],"height:1.3612em;vertical-align:-0.4811em;",[574,2304,2306,2309,2375],{"className":2305},[618],[574,2307],{"className":2308},[826,827],[574,2310,2312],{"className":2311},[772],[574,2313,2315,2366],{"className":2314},[720,834],[574,2316,2318,2363],{"className":2317},[724],[574,2319,2321,2338,2346],{"className":2320,"style":987},[728],[574,2322,2323,2326],{"style":844},[574,2324],{"className":2325,"style":848},[735],[574,2327,2329],{"className":2328},[740,741,742,743],[574,2330,2332],{"className":2331},[618,743],[574,2333,2335],{"className":2334},[618,1147,743],[574,2336,628],{"className":2337},[618,743],[574,2339,2340,2343],{"style":860},[574,2341],{"className":2342,"style":848},[735],[574,2344],{"className":2345,"style":868},[867],[574,2347,2348,2351],{"style":871},[574,2349],{"className":2350,"style":848},[735],[574,2352,2354],{"className":2353},[740,741,742,743],[574,2355,2357],{"className":2356},[618,743],[574,2358,2360],{"className":2359},[618,1147,743],[574,2361,632],{"className":2362},[618,743],[574,2364,888],{"className":2365},[887],[574,2367,2369],{"className":2368},[724],[574,2370,2373],{"className":2371,"style":2372},[728],"height:0.4811em;",[574,2374],{},[574,2376],{"className":2377},[901,827]," ist nicht ",[574,2380,2382,2400],{"className":2381},[577],[574,2383,2385],{"className":2384},[581],[583,2386,2387],{"xmlns":585},[587,2388,2389,2397],{},[590,2390,2391,2393,2395],{},[593,2392,763],{},[653,2394,766],{},[593,2396,595],{},[597,2398,2399],{"encoding":599},"\\tan \\alpha",[574,2401,2403],{"className":2402,"ariaHidden":605},[604],[574,2404,2406,2409,2412,2415],{"className":2405},[609],[574,2407],{"className":2408,"style":792},[613],[574,2410,763],{"className":2411},[796],[574,2413],{"className":2414,"style":800},[686],[574,2416,595],{"className":2417,"style":620},[618,619],", sondern ",[574,2420,2422,2446],{"className":2421},[577],[574,2423,2425],{"className":2424},[581],[583,2426,2427],{"xmlns":585},[587,2428,2429,2443],{},[590,2430,2431],{},[772,2432,2433,2435],{},[660,2434,1056],{},[590,2436,2437,2439,2441],{},[593,2438,763],{},[653,2440,766],{},[593,2442,595],{},[597,2444,2445],{"encoding":599},"\\frac{1}{\\tan \\alpha}",[574,2447,2449],{"className":2448,"ariaHidden":605},[604],[574,2450,2452,2456],{"className":2451},[609],[574,2453],{"className":2454,"style":2455},[613],"height:1.1901em;vertical-align:-0.345em;",[574,2457,2459,2462,2540],{"className":2458},[618],[574,2460],{"className":2461},[826,827],[574,2463,2465],{"className":2464},[772],[574,2466,2468,2532],{"className":2467},[720,834],[574,2469,2471,2529],{"className":2470},[724],[574,2472,2475,2507,2515],{"className":2473,"style":2474},[728],"height:0.8451em;",[574,2476,2477,2480],{"style":844},[574,2478],{"className":2479,"style":848},[735],[574,2481,2483],{"className":2482},[740,741,742,743],[574,2484,2486,2500,2504],{"className":2485},[618,743],[574,2487,2489,2493,2496],{"className":2488},[796,743],[574,2490,2492],{"className":2491},[743],"t",[574,2494,776],{"className":2495},[743],[574,2497,2499],{"className":2498},[743],"n",[574,2501],{"className":2502,"style":2503},[686,743],"margin-right:0.1952em;",[574,2505,595],{"className":2506,"style":620},[618,619,743],[574,2508,2509,2512],{"style":860},[574,2510],{"className":2511,"style":848},[735],[574,2513],{"className":2514,"style":868},[867],[574,2516,2517,2520],{"style":871},[574,2518],{"className":2519,"style":848},[735],[574,2521,2523],{"className":2522},[740,741,742,743],[574,2524,2526],{"className":2525},[618,743],[574,2527,1056],{"className":2528},[618,743],[574,2530,888],{"className":2531},[887],[574,2533,2535],{"className":2534},[724],[574,2536,2538],{"className":2537,"style":895},[728],[574,2539],{},[574,2541],{"className":2542},[901,827],[2269,2544,2545,2546,2574,2575,2661,2662,1038],{},"Annehmen, der Tangens könne nicht größer als ",[574,2547,2549,2562],{"className":2548},[577],[574,2550,2552],{"className":2551},[581],[583,2553,2554],{"xmlns":585},[587,2555,2556,2560],{},[590,2557,2558],{},[660,2559,1056],{},[597,2561,1056],{"encoding":599},[574,2563,2565],{"className":2564,"ariaHidden":605},[604],[574,2566,2568,2571],{"className":2567},[609],[574,2569],{"className":2570,"style":1068},[613],[574,2572,1056],{"className":2573},[618]," sein. Für ",[574,2576,2578,2601],{"className":2577},[577],[574,2579,2581],{"className":2580},[581],[583,2582,2583],{"xmlns":585},[587,2584,2585,2598],{},[590,2586,2587,2589,2592],{},[593,2588,595],{},[653,2590,2591],{},">",[657,2593,2594,2596],{},[660,2595,1326],{},[653,2597,665],{},[597,2599,2600],{"encoding":599},"\\alpha > 45^\\circ",[574,2602,2604,2623],{"className":2603,"ariaHidden":605},[604],[574,2605,2607,2611,2614,2617,2620],{"className":2606},[609],[574,2608],{"className":2609,"style":2610},[613],"height:0.5782em;vertical-align:-0.0391em;",[574,2612,595],{"className":2613,"style":620},[618,619],[574,2615],{"className":2616,"style":687},[686],[574,2618,2591],{"className":2619},[691],[574,2621],{"className":2622,"style":687},[686],[574,2624,2626,2629,2632],{"className":2625},[609],[574,2627],{"className":2628,"style":701},[613],[574,2630,1362],{"className":2631},[618],[574,2633,2635,2638],{"className":2634},[618],[574,2636,1369],{"className":2637},[618],[574,2639,2641],{"className":2640},[716],[574,2642,2644],{"className":2643},[720],[574,2645,2647],{"className":2646},[724],[574,2648,2650],{"className":2649,"style":701},[728],[574,2651,2652,2655],{"style":731},[574,2653],{"className":2654,"style":736},[735],[574,2656,2658],{"className":2657},[740,741,742,743],[574,2659,665],{"className":2660},[747,743]," ist ",[574,2663,2665,2687],{"className":2664},[577],[574,2666,2668],{"className":2667},[581],[583,2669,2670],{"xmlns":585},[587,2671,2672,2684],{},[590,2673,2674,2676,2678,2680,2682],{},[593,2675,763],{},[653,2677,766],{},[593,2679,595],{},[653,2681,2591],{},[660,2683,1056],{},[597,2685,2686],{"encoding":599},"\\tan \\alpha > 1",[574,2688,2690,2715],{"className":2689,"ariaHidden":605},[604],[574,2691,2693,2697,2700,2703,2706,2709,2712],{"className":2692},[609],[574,2694],{"className":2695,"style":2696},[613],"height:0.6542em;vertical-align:-0.0391em;",[574,2698,763],{"className":2699},[796],[574,2701],{"className":2702,"style":800},[686],[574,2704,595],{"className":2705,"style":620},[618,619],[574,2707],{"className":2708,"style":687},[686],[574,2710,2591],{"className":2711},[691],[574,2713],{"className":2714,"style":687},[686],[574,2716,2718,2721],{"className":2717},[609],[574,2719],{"className":2720,"style":1068},[613],[574,2722,1056],{"className":2723},[618],[2269,2725,2726,2727,2769,2770,2840,2841,2936,2937,1038],{},"Eine Steigung in Prozent direkt als Winkel lesen: ",[574,2728,2730,2750],{"className":2729},[577],[574,2731,2733],{"className":2732},[581],[583,2734,2735],{"xmlns":585},[587,2736,2737,2747],{},[590,2738,2739,2741,2743],{},[660,2740,2106],{},[1098,2742,1513],{},[593,2744,2746],{"mathvariant":2745},"normal","%",[597,2748,2749],{"encoding":599},"12\\,\\%",[574,2751,2753],{"className":2752,"ariaHidden":605},[604],[574,2754,2756,2760,2763,2766],{"className":2755},[609],[574,2757],{"className":2758,"style":2759},[613],"height:0.8056em;vertical-align:-0.0556em;",[574,2761,2106],{"className":2762},[618],[574,2764],{"className":2765,"style":800},[686],[574,2767,2746],{"className":2768},[618]," Steigung bedeutet ",[574,2771,2773,2795],{"className":2772},[577],[574,2774,2776],{"className":2775},[581],[583,2777,2778],{"xmlns":585},[587,2779,2780,2792],{},[590,2781,2782,2784,2786,2788,2790],{},[593,2783,763],{},[653,2785,766],{},[593,2787,595],{},[653,2789,655],{},[660,2791,1924],{},[597,2793,2794],{"encoding":599},"\\tan \\alpha = 0{,}12",[574,2796,2798,2822],{"className":2797,"ariaHidden":605},[604],[574,2799,2801,2804,2807,2810,2813,2816,2819],{"className":2800},[609],[574,2802],{"className":2803,"style":792},[613],[574,2805,763],{"className":2806},[796],[574,2808],{"className":2809,"style":800},[686],[574,2811,595],{"className":2812,"style":620},[618,619],[574,2814],{"className":2815,"style":687},[686],[574,2817,655],{"className":2818},[691],[574,2820],{"className":2821,"style":687},[686],[574,2823,2825,2828,2831,2837],{"className":2824},[609],[574,2826],{"className":2827,"style":1765},[613],[574,2829,712],{"className":2830},[618],[574,2832,2834],{"className":2833},[618],[574,2835,1777],{"className":2836},[1776],[574,2838,2106],{"className":2839},[618],", also ",[574,2842,2844,2866],{"className":2843},[577],[574,2845,2847],{"className":2846},[581],[583,2848,2849],{"xmlns":585},[587,2850,2851,2863],{},[590,2852,2853,2855,2857],{},[593,2854,595],{},[653,2856,1647],{},[657,2858,2859,2861],{},[660,2860,1967],{},[653,2862,665],{},[597,2864,2865],{"encoding":599},"\\alpha \\approx 6{,}84^\\circ",[574,2867,2869,2888],{"className":2868,"ariaHidden":605},[604],[574,2870,2872,2876,2879,2882,2885],{"className":2871},[609],[574,2873],{"className":2874,"style":2875},[613],"height:0.4831em;",[574,2877,595],{"className":2878,"style":620},[618,619],[574,2880],{"className":2881,"style":687},[686],[574,2883,1647],{"className":2884},[691],[574,2886],{"className":2887,"style":687},[686],[574,2889,2891,2895,2898,2904,2907],{"className":2890},[609],[574,2892],{"className":2893,"style":2894},[613],"height:0.8686em;vertical-align:-0.1944em;",[574,2896,2221],{"className":2897},[618],[574,2899,2901],{"className":2900},[618],[574,2902,1777],{"className":2903},[1776],[574,2905,2231],{"className":2906},[618],[574,2908,2910,2913],{"className":2909},[618],[574,2911,1362],{"className":2912},[618],[574,2914,2916],{"className":2915},[716],[574,2917,2919],{"className":2918},[720],[574,2920,2922],{"className":2921},[724],[574,2923,2925],{"className":2924,"style":701},[728],[574,2926,2927,2930],{"style":731},[574,2928],{"className":2929,"style":736},[735],[574,2931,2933],{"className":2932},[740,741,742,743],[574,2934,665],{"className":2935},[747,743],", nicht ",[574,2938,2940,2958],{"className":2939},[577],[574,2941,2943],{"className":2942},[581],[583,2944,2945],{"xmlns":585},[587,2946,2947,2955],{},[590,2948,2949],{},[657,2950,2951,2953],{},[660,2952,2106],{},[653,2954,665],{},[597,2956,2957],{"encoding":599},"12^\\circ",[574,2959,2961],{"className":2960,"ariaHidden":605},[604],[574,2962,2964,2967,2970],{"className":2963},[609],[574,2965],{"className":2966,"style":701},[613],[574,2968,1056],{"className":2969},[618],[574,2971,2973,2976],{"className":2972},[618],[574,2974,1880],{"className":2975},[618],[574,2977,2979],{"className":2978},[716],[574,2980,2982],{"className":2981},[720],[574,2983,2985],{"className":2984},[724],[574,2986,2988],{"className":2987,"style":701},[728],[574,2989,2990,2993],{"style":731},[574,2991],{"className":2992,"style":736},[735],[574,2994,2996],{"className":2995},[740,741,742,743],[574,2997,665],{"className":2998},[747,743],[2269,3000,3001,3002,3006,3007,3010],{},"Den Taschenrechner im Bogenmaß (",[3003,3004,3005],"code",{},"RAD",") statt im Gradmaß (",[3003,3008,3009],{},"DEG",") rechnen lassen.",{"title":3012,"searchDepth":3013,"depth":3013,"links":3014},"",2,[3015,3016,3017],{"id":562,"depth":3013,"text":563},{"id":1301,"depth":3013,"text":1302},{"id":2263,"depth":3013,"text":2264},[3019,3022,3024,3026,3029],{"lhs":3020,"rhs":3021},"tan(atan2(a, b))","a\u002Fb",{"lhs":3023,"rhs":1056},"tan(45*pi\u002F180)",{"lhs":3025,"rhs":1769},"round(20 * tan(35*pi\u002F180), 1)",{"lhs":3027,"rhs":3028},"1.2\u002F10","0.12",{"lhs":3030,"rhs":3031},"round(atan(0.12) * 180\u002Fpi, 2)","6.84","\\text{rechtwinkliges Dreieck},\\ 0^\\circ \u003C \\alpha \u003C 90^\\circ","\u003Cspan class=\"katex\">rechtwinkliges\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Dreieck\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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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:0.2778em;\">\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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