\(\sin{0^\circ}=0\)
\(\cos{0^\circ}=1\)
\(\tan{0^\circ}=0\)
\(\sin{3^\circ}=\dfrac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2} }{16}-\dfrac{\sqrt{30}-\sqrt{10}+\sqrt{6}-\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }\)
\(\cos{3^\circ}=\dfrac{\sqrt{30}-\sqrt{10}-\sqrt{6}+\sqrt{2} }{16}+\dfrac{\sqrt{30}+\sqrt{10}+\sqrt{6}+\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }\)
\(\tan{3^\circ}=2+\sqrt{5}+\sqrt{15+6\sqrt{5} }-\dfrac{3\sqrt{3}+\sqrt{15}+\sqrt{5+2\sqrt{5} }+\sqrt{25+10\sqrt{5} }}{2}\)
\(\sin{6^\circ}=\dfrac{\sqrt{30-6\sqrt{5} }-1-\sqrt{5} }{8}\)
\(\cos{6^\circ}=\dfrac{\sqrt{15}+\sqrt{3}+\sqrt{10-2\sqrt{5} }}{8}\)
\(\tan{6^\circ}=\dfrac{\sqrt{3}-\sqrt{15}+\sqrt{10-2\sqrt{5} }}{2}\)
\(\sin{9^\circ}=\dfrac{1}{4}\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
\(\sin{15^\circ}=\dfrac{1}{4}\sqrt{6}-\dfrac{1}{4}\sqrt{2}\)
\(\cos{15^\circ}=\dfrac{1}{4}\sqrt{6}+\dfrac{1}{4}\sqrt{2}\)
\(\tan{15^\circ}=2-\sqrt{3}\)
\(\sin{18^\circ}=\dfrac{-1+\sqrt{5} }{4}\)
\(\cos{18^\circ}=\dfrac{\sqrt{10+2\sqrt{5} }}{4}\)
\(\tan{18^\circ}=\dfrac{\sqrt{25-10\sqrt{5} }}{5}\)
\(\sin{22.5^\circ}=\dfrac{\sqrt{2-\sqrt{2} }}{2}\)
\(\cos{22.5^\circ}=\dfrac{\sqrt{2+\sqrt{2} }}{2}\)
\(\tan{22.5^\circ}=\sqrt{2}-1\)
\(\sin{30^\circ}=\dfrac{1}{2}\)
\(\cos{30^\circ}=\dfrac{\sqrt{3} }{2}\)
\(\tan{30^\circ}=\dfrac{\sqrt{3} }{3}\)
\(\sin{36^\circ}=\dfrac{\sqrt{10-2\sqrt{5} }}{4}\)
\(\cos{36^\circ}=\dfrac{1+\sqrt{5} }{4}\)
\(\tan{36^\circ}=\sqrt{5-2\sqrt{5} }\)
\(\sin{37.5^\circ}=\dfrac{\sqrt{8-2\sqrt{6}+2\sqrt{2} }}{4}\)
\(\cos{37.5^\circ}=\dfrac{\sqrt{8+2\sqrt{6}-2\sqrt{2} }}{4}\)
\(\tan{37.5^\circ}=\sqrt{15-6\sqrt{6}-8\sqrt{3}+10\sqrt{2} }\)
\(\sin{45^\circ}=\dfrac{\sqrt{2} }{2}\)
\(\cos{45^\circ}=\dfrac{\sqrt{2} }{2}\)
\(\tan{45^\circ}=1\)
\(\sin{54^\circ}=\dfrac{1+\sqrt{5} }{4}\)
\(\cos{54^\circ}=\dfrac{\sqrt{10-2\sqrt{5} }}{4}\)
\(\tan{54^\circ}=\sqrt{5-2\sqrt{5} }+\dfrac{2\sqrt{25-10\sqrt{5} }}{5}\)
\(\sin{60^\circ}=\dfrac{\sqrt{3} }{2}\)
\(\cos{60^\circ}=\dfrac{1}{2}\)
\(\tan{60^\circ}=\sqrt{3}\)
\(\sin{72^\circ}=\dfrac{\sqrt{10+2\sqrt{5} }}{4}\)
\(\cos{72^\circ}=\dfrac{\sqrt{5}-1}{4}\)
\(\tan{72^\circ}=\sqrt{5+2\sqrt{5} }\)
\(\sin{75^\circ}=\dfrac{\sqrt{6}+\sqrt{2} }{4}\)
\(\cos{75^\circ}=\dfrac{\sqrt{6}-\sqrt{2} }{4}\)
\(\tan{75^\circ}=2+\sqrt{3}\)
\(\sin{84^\circ}=\dfrac{1}{8}\sqrt{15}+\dfrac{1}{8}\sqrt{3}+\dfrac{1}{8}\sqrt{10-2\sqrt{5}}\)
\(\cos{84^\circ}=\dfrac{\sqrt{30-6\sqrt{5} }-1-\sqrt{5} }{8}\)
\(\sin{87^\circ}=\dfrac{\sqrt{30}-\sqrt{10}-\sqrt{6}+\sqrt{2} }{16}+\dfrac{\sqrt{30}+\sqrt{10}+\sqrt{6}+\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }\)
\(\cos{87^\circ}=\dfrac{\sqrt{30}+\sqrt{10}-\sqrt{6}-\sqrt{2} }{16}-\dfrac{\sqrt{30}-\sqrt{10}+\sqrt{6}-\sqrt{2} }{32}\sqrt{10-2\sqrt{5} }\)
\(\sin{90^\circ}=1\)
\(\cos{90^\circ}=0\)