特殊三角函数值
zhanghengrui
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个人记录
\sin{0^\circ}=0
\cos{0^\circ}=1
\tan{0^\circ}=0
\sin{3^\circ}=\dfrac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2} }{16}-\dfrac{\sqrt{30}-\sqrt{10}+\sqrt{6}-\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }
\cos{3^\circ}=\dfrac{\sqrt{30}-\sqrt{10}-\sqrt{6}+\sqrt{2} }{16}+\dfrac{\sqrt{30}+\sqrt{10}+\sqrt{6}+\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }
\tan{3^\circ}=2+\sqrt{5}+\sqrt{15+6\sqrt{5} }-\dfrac{3\sqrt{3}+\sqrt{15}+\sqrt{5+2\sqrt{5} }+\sqrt{25+10\sqrt{5} }}{2}
\sin{6^\circ}=\dfrac{\sqrt{30-6\sqrt{5} }-1-\sqrt{5} }{8}
\cos{6^\circ}=\dfrac{\sqrt{15}+\sqrt{3}+\sqrt{10-2\sqrt{5} }}{8}
\tan{6^\circ}=\dfrac{\sqrt{3}-\sqrt{15}+\sqrt{10-2\sqrt{5} }}{2}
\sin{9^\circ}=\dfrac{1}{4}\sqrt{8-2\sqrt{10+2\sqrt{5}}}
\sin{15^\circ}=\dfrac{1}{4}\sqrt{6}-\dfrac{1}{4}\sqrt{2}
\cos{15^\circ}=\dfrac{1}{4}\sqrt{6}+\dfrac{1}{4}\sqrt{2}
\tan{15^\circ}=2-\sqrt{3}
\sin{18^\circ}=\dfrac{-1+\sqrt{5} }{4}
\cos{18^\circ}=\dfrac{\sqrt{10+2\sqrt{5} }}{4}
\tan{18^\circ}=\dfrac{\sqrt{25-10\sqrt{5} }}{5}
\sin{22.5^\circ}=\dfrac{\sqrt{2-\sqrt{2} }}{2}
\cos{22.5^\circ}=\dfrac{\sqrt{2+\sqrt{2} }}{2}
\tan{22.5^\circ}=\sqrt{2}-1
\sin{30^\circ}=\dfrac{1}{2}
\cos{30^\circ}=\dfrac{\sqrt{3} }{2}
\tan{30^\circ}=\dfrac{\sqrt{3} }{3}
\sin{36^\circ}=\dfrac{\sqrt{10-2\sqrt{5} }}{4}
\cos{36^\circ}=\dfrac{1+\sqrt{5} }{4}
\tan{36^\circ}=\sqrt{5-2\sqrt{5} }
\sin{37.5^\circ}=\dfrac{\sqrt{8-2\sqrt{6}+2\sqrt{2} }}{4}
\cos{37.5^\circ}=\dfrac{\sqrt{8+2\sqrt{6}-2\sqrt{2} }}{4}
\tan{37.5^\circ}=\sqrt{15-6\sqrt{6}-8\sqrt{3}+10\sqrt{2} }
\sin{45^\circ}=\dfrac{\sqrt{2} }{2}
\cos{45^\circ}=\dfrac{\sqrt{2} }{2}
\tan{45^\circ}=1
\sin{54^\circ}=\dfrac{1+\sqrt{5} }{4}
\cos{54^\circ}=\dfrac{\sqrt{10-2\sqrt{5} }}{4}
\tan{54^\circ}=\sqrt{5-2\sqrt{5} }+\dfrac{2\sqrt{25-10\sqrt{5} }}{5}
\sin{60^\circ}=\dfrac{\sqrt{3} }{2}
\cos{60^\circ}=\dfrac{1}{2}
\tan{60^\circ}=\sqrt{3}
\sin{72^\circ}=\dfrac{\sqrt{10+2\sqrt{5} }}{4}
\cos{72^\circ}=\dfrac{\sqrt{5}-1}{4}
\tan{72^\circ}=\sqrt{5+2\sqrt{5} }
\sin{75^\circ}=\dfrac{\sqrt{6}+\sqrt{2} }{4}
\cos{75^\circ}=\dfrac{\sqrt{6}-\sqrt{2} }{4}
\tan{75^\circ}=2+\sqrt{3}
\sin{84^\circ}=\dfrac{1}{8}\sqrt{15}+\dfrac{1}{8}\sqrt{3}+\dfrac{1}{8}\sqrt{10-2\sqrt{5}}
\cos{84^\circ}=\dfrac{\sqrt{30-6\sqrt{5} }-1-\sqrt{5} }{8}
\sin{87^\circ}=\dfrac{\sqrt{30}-\sqrt{10}-\sqrt{6}+\sqrt{2} }{16}+\dfrac{\sqrt{30}+\sqrt{10}+\sqrt{6}+\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }
\cos{87^\circ}=\dfrac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2} }{16}-\dfrac{\sqrt{30}-\sqrt{10}+\sqrt{6}-\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }
\sin{90^\circ}=1
\cos{90^\circ}=0