Template:Trigonometric Functions Exact Values Table

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Exact values of common angles

Radian	Degree	sin	cos	tan	cot	sec	csc
$0$	$0^{\circ }$	$0$	$1$	$0$	$\infty$	$1$	$\infty$
${\frac {\pi }{24}}$	$7.5^{\circ }$	${\frac {1}{2}}{\sqrt {2-{\sqrt {2+{\sqrt {3}}}}}}$	${\frac {1}{2}}{\sqrt {2+{\sqrt {2+{\sqrt {3}}}}}}$	${\sqrt {6}}-2-{\sqrt {5-2{\sqrt {6}}}}$	${\sqrt {6}}+2+{\sqrt {5+2{\sqrt {6}}}}$	${\sqrt {2}}{\sqrt {8-3{\sqrt {6}}-{\sqrt {2(49-20{\sqrt {6}})}}}}$	${\sqrt {2}}{\sqrt {8+3{\sqrt {6}}+{\sqrt {2(49+20{\sqrt {6}})}}}}$
${\frac {\pi }{12}}$	$15^{\circ }$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	$2-{\sqrt {3}}$	$2+{\sqrt {3}}$	${\sqrt {2}}({\sqrt {3}}-1)$	${\sqrt {2}}({\sqrt {3}}+1)$
${\frac {\pi }{10}}$	$18^{\circ }$	${\frac {{\sqrt {5}}-1}{4}}$	${\frac {\sqrt {10+2{\sqrt {5}}}}{4}}$	${\frac {\sqrt {25-10{\sqrt {5}}}}{5}}$	${\sqrt {5+2{\sqrt {5}}}}$	${\frac {\sqrt {50-10{\sqrt {5}}}}{5}}$	$1+{\sqrt {5}}$
${\frac {\pi }{8}}$	$22.5^{\circ }$	${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$	${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$	${\sqrt {2}}-1$	${\sqrt {2}}+1$	${\sqrt {4-2{\sqrt {2}}}}$	${\sqrt {4+2{\sqrt {2}}}}$
${\frac {\pi }{6}}$	$30^{\circ }$	${\frac {1}{2}}$	${\frac {\sqrt {3}}{2}}$	${\frac {\sqrt {3}}{3}}$	${\sqrt {3}}$	${\frac {2{\sqrt {3}}}{3}}$	$2$
${\frac {\pi }{5}}$	$36^{\circ }$	${\frac {\sqrt {10-2{\sqrt {5}}}}{4}}$	${\frac {1+{\sqrt {5}}}{4}}$	${\sqrt {5-2{\sqrt {5}}}}$	${\frac {\sqrt {25+10{\sqrt {5}}}}{5}}$	${\sqrt {5}}-1$	${\frac {\sqrt {50+10{\sqrt {5}}}}{5}}$
${\frac {\pi }{4}}$	$45^{\circ }$	${\frac {\sqrt {2}}{2}}$	${\frac {\sqrt {2}}{2}}$	$1$	$1$	${\sqrt {2}}$	${\sqrt {2}}$
${\frac {3\pi }{10}}$	$54^{\circ }$	${\frac {1+{\sqrt {5}}}{4}}$	${\frac {\sqrt {10-2{\sqrt {5}}}}{4}}$	${\frac {\sqrt {25+10{\sqrt {5}}}}{5}}$	${\sqrt {5-2{\sqrt {5}}}}$	${\frac {\sqrt {50+10{\sqrt {5}}}}{5}}$	${\sqrt {5}}-1$
${\frac {\pi }{3}}$	$60^{\circ }$	${\frac {\sqrt {3}}{2}}$	${\frac {1}{2}}$	${\sqrt {3}}$	${\frac {\sqrt {3}}{3}}$	$2$	${\frac {2{\sqrt {3}}}{3}}$
${\frac {3\pi }{8}}$	$67.5^{\circ }$	${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$	${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$	${\sqrt {2}}+1$	${\sqrt {2}}-1$	${\sqrt {4+2{\sqrt {2}}}}$	${\sqrt {4-2{\sqrt {2}}}}$
${\frac {2\pi }{5}}$	$72^{\circ }$	${\frac {\sqrt {10+2{\sqrt {5}}}}{4}}$	${\frac {{\sqrt {5}}-1}{4}}$	${\sqrt {5+2{\sqrt {5}}}}$	${\frac {\sqrt {25-10{\sqrt {5}}}}{5}}$	$1+{\sqrt {5}}$	${\frac {\sqrt {50-10{\sqrt {5}}}}{5}}$
${\frac {5\pi }{12}}$	$75^{\circ }$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	$2+{\sqrt {3}}$	$2-{\sqrt {3}}$	${\sqrt {2}}({\sqrt {3}}+1)$	${\sqrt {2}}({\sqrt {3}}-1)$
${\frac {\pi }{2}}$	$90^{\circ }$	$1$	$0$	$\infty$	$0$	$\infty$	$1$
${\frac {7\pi }{12}}$	$105^{\circ }$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	$-2-{\sqrt {3}}$	$-2+{\sqrt {3}}$	$-{\sqrt {2}}(1+{\sqrt {3}})$	${\sqrt {2}}({\sqrt {3}}-1)$
${\frac {2\pi }{3}}$	$120^{\circ }$	${\frac {\sqrt {3}}{2}}$	$-{\frac {1}{2}}$	$-{\sqrt {3}}$	$-{\frac {\sqrt {3}}{3}}$	$-2$	${\frac {2{\sqrt {3}}}{3}}$
${\frac {3\pi }{4}}$	$135^{\circ }$	${\frac {\sqrt {2}}{2}}$	$-{\frac {\sqrt {2}}{2}}$	$-1$	$-1$	$-{\sqrt {2}}$	${\sqrt {2}}$
${\frac {5\pi }{6}}$	$150^{\circ }$	${\frac {1}{2}}$	$-{\frac {\sqrt {3}}{2}}$	$-{\frac {\sqrt {3}}{3}}$	$-{\sqrt {3}}$	$-{\frac {2{\sqrt {3}}}{3}}$	$2$
${\frac {11\pi }{12}}$	$165^{\circ }$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	$-2-{\sqrt {3}}$	$-2+{\sqrt {3}}$	$-{\sqrt {2}}({\sqrt {3}}-1)$	${\sqrt {2}}({\sqrt {3}}+1)$
$\pi$	$180^{\circ }$	$0$	$-1$	$0$	$\infty$	$-1$	$\infty$
${\frac {13\pi }{12}}$	$195^{\circ }$	$-{\frac {{\sqrt {3}}-1}{2{\sqrt {2}}}}$	$-{\frac {{\sqrt {3}}+1}{2{\sqrt {2}}}}$	$2-{\sqrt {3}}$	$2+{\sqrt {3}}$	$-{\sqrt {2}}({\sqrt {3}}-1)$	$-{\sqrt {2}}(1+{\sqrt {3}})$
${\frac {7\pi }{6}}$	$210^{\circ }$	$-{\frac {1}{2}}$	$-{\frac {\sqrt {3}}{2}}$	${\frac {\sqrt {3}}{3}}$	${\sqrt {3}}$	$-{\frac {2{\sqrt {3}}}{3}}$	$-2$
${\frac {5\pi }{4}}$	$225^{\circ }$	$-{\dfrac {\sqrt {2}}{2}}$	$-{\dfrac {\sqrt {2}}{2}}$	$1$	$1$	$-{\sqrt {2}}$	$-{\sqrt {2}}$
${\frac {4\pi }{3}}$	$240^{\circ }$	$-{\frac {\sqrt {3}}{2}}$	$-{\frac {1}{2}}$	${\sqrt {3}}$	${\frac {\sqrt {3}}{3}}$	$-2$	$-{\frac {2{\sqrt {3}}}{3}}$
${\frac {17\pi }{12}}$	$255^{\circ }$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	$2+{\sqrt {3}}$	$2-{\sqrt {3}}$	$-{\sqrt {2}}({\sqrt {3}}+1)$	$-{\sqrt {2}}({\sqrt {3}}-1)$
${\frac {3\pi }{2}}$	$270^{\circ }$	$-1$	$0$	$\infty$	$0$	$\infty$	$-1$
${\frac {19\pi }{12}}$	$285^{\circ }$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	$-2+{\sqrt {3}}$	$-2+{\sqrt {3}}$	${\sqrt {2}}({\sqrt {3}}+1)$	$-{\sqrt {2}}({\sqrt {3}}-1)$
${\frac {5\pi }{3}}$	$300^{\circ }$	$-{\frac {\sqrt {3}}{2}}$	${\frac {1}{2}}$	$-{\sqrt {3}}$	$-{\frac {\sqrt {3}}{3}}$	$2$	$-{\frac {2{\sqrt {3}}}{3}}$
${\frac {7\pi }{4}}$	$315^{\circ }$	$-{\frac {\sqrt {2}}{2}}$	${\frac {\sqrt {2}}{2}}$	$-1$	$-1$	${\sqrt {2}}$	$-{\sqrt {2}}$
${\frac {11\pi }{6}}$	$330^{\circ }$	$-{\frac {1}{2}}$	${\frac {\sqrt {3}}{2}}$	$-{\frac {\sqrt {3}}{3}}$	$-{\sqrt {3}}$	${\frac {2{\sqrt {3}}}{3}}$	$-2$
${\frac {23\pi }{12}}$	$345^{\circ }$	$-{\frac {\sqrt {2}}{4}}({\sqrt {3}}-1)$	${\frac {\sqrt {2}}{4}}({\sqrt {3}}+1)$	$-2+{\sqrt {3}}$	$-2-{\sqrt {3}}$	${\sqrt {2}}({\sqrt {3}}-1)$	$-{\sqrt {2}}({\sqrt {3}}+1)$

See also

• Exact trigonometric values
• List of trigonometric identities
• Template:DomainsImagesAndPrototypesOfTrigAndInverseTrigFunctions
• Template:Trigonometry

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