$\theta$ (positive)

$\sin(\theta )$

$\cos(\theta )$

$\tan(\theta )$

$\cot(\theta )$

$\sec(\theta )$

$\csc(\theta )$

$\theta$ (negative)

(degrees) 
(radians)

(degrees) 
(radians)

$0^{\circ }$ 
$0$

$0$

$1$

$0$

not defined

$1$

not defined

$360^{\circ }$ 
$2\pi$

$15^{\circ }$ 
${\frac {\pi }{12}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

$2{\sqrt {3}}$

$2+{\sqrt {3}}$

${\sqrt {6}}{\sqrt {2}}$

${\sqrt {6}}+{\sqrt {2}}$

$345^{\circ }$ 
${\frac {13\pi }{12}}$

$22.5^{\circ }$ 
${\frac {\pi }{8}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\sqrt {2}}1$

${\sqrt {2}}+1$

${\sqrt {42{\sqrt {2}}}}$

${\sqrt {4+2{\sqrt {2}}}}$

$337.5^{\circ }$ 
${\frac {15\pi }{8}}$

$30^{\circ }$ 
${\frac {\pi }{6}}$

${\frac {1}{2}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{\sqrt {3}}}$

${\sqrt {3}}$

${\frac {2}{\sqrt {3}}}$

$2$

$330^{\circ }$ 
${\frac {11\pi }{6}}$

$45^{\circ }$ 
${\frac {\pi }{4}}$

${\frac {1}{\sqrt {2}}}$

$1$

${\sqrt {2}}$

$315^{\circ }$ 
${\frac {7\pi }{4}}$

$60^{\circ }$ 
${\frac {\pi }{3}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{2}}$

${\sqrt {3}}$

${\frac {1}{\sqrt {3}}}$

$2$

${\frac {2}{\sqrt {3}}}$

$300^{\circ }$ 
${\frac {5\pi }{3}}$

$67.5^{\circ }$ 
${\frac {3\pi }{8}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\sqrt {2}}+1$

${\sqrt {2}}1$

${\sqrt {4+2{\sqrt {2}}}}$

${\sqrt {42{\sqrt {2}}}}$

$292.5^{\circ }$ 
${\frac {11\pi }{8}}$

$75^{\circ }$ 
${\frac {5\pi }{12}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

$2+{\sqrt {3}}$

$2{\sqrt {3}}$

${\sqrt {6}}+{\sqrt {2}}$

${\sqrt {6}}{\sqrt {2}}$

$285^{\circ }$ 
${\frac {19\pi }{12}}$

$90^{\circ }$ 
${\frac {\pi }{2}}$

$1$

$0$

not defined

$0$

not defined

$1$

$270^{\circ }$ 
${\frac {3\pi }{2}}$

$105^{\circ }$ 
${\frac {7\pi }{12}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

$2{\sqrt {3}}$

$2+{\sqrt {3}}$

${\sqrt {6}}{\sqrt {2}}$

${\sqrt {6}}{\sqrt {2}}$

$255^{\circ }$ 
${\frac {17\pi }{12}}$

$112.5^{\circ }$ 
${\frac {5\pi }{8}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\sqrt {2}}1$

${\sqrt {2}}+1$

${\sqrt {4+2{\sqrt {2}}}}$

${\sqrt {42{\sqrt {2}}}}$

$247.5^{\circ }$ 
${\frac {11\pi }{8}}$

$120^{\circ }$ 
${\frac {2\pi }{3}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{2}}$

${\sqrt {3}}$

${\frac {1}{\sqrt {3}}}$

$2$

${\frac {2}{\sqrt {3}}}$

$240^{\circ }$ 
${\frac {4\pi }{3}}$

$135^{\circ }$ 
${\frac {3\pi }{4}}$

${\frac {1}{\sqrt {2}}}$

${\frac {1}{\sqrt {2}}}$

$1$

${\sqrt {2}}$

${\sqrt {2}}$

$225^{\circ }$ 
${\frac {5\pi }{4}}$

$150^{\circ }$ 
${\frac {5\pi }{6}}$

${\frac {1}{2}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{\sqrt {3}}}$

${\sqrt {3}}$

${\frac {2}{\sqrt {3}}}$

$2$

$210^{\circ }$ 
${\frac {7\pi }{6}}$

$157.5^{\circ }$ 
${\frac {7\pi }{8}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\sqrt {2}}+1$

${\sqrt {2}}1$

${\sqrt {42{\sqrt {2}}}}$

${\sqrt {4+2{\sqrt {2}}}}$

$202.5^{\circ }$ 
${\frac {9\pi }{8}}$

$165^{\circ }$ 
${\frac {11\pi }{12}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

$2+{\sqrt {3}}$

$2{\sqrt {3}}$

${\sqrt {6}}+{\sqrt {2}}$

${\sqrt {6}}+{\sqrt {2}}$

$195^{\circ }$ 
${\frac {13\pi }{12}}$

$180^{\circ }$ 
$\pi$

$0$

$1$

$0$

not defined

$1$

not defined

$180^{\circ }$ 
$\pi$

$195^{\circ }$ 
${\frac {13\pi }{12}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

$2{\sqrt {3}}$

$2+{\sqrt {3}}$

${\sqrt {6}}+{\sqrt {2}}$

${\sqrt {6}}{\sqrt {2}}$

$165^{\circ }$ 
${\frac {11\pi }{12}}$

$202.5^{\circ }$ 
${\frac {9\pi }{8}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\sqrt {2}}1$

${\sqrt {2}}+1$

${\sqrt {42{\sqrt {2}}}}$

${\sqrt {4+2{\sqrt {2}}}}$

$157.5^{\circ }$ 
${\frac {7\pi }{8}}$

$210^{\circ }$ 
${\frac {7\pi }{6}}$

${\frac {1}{2}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{\sqrt {3}}}$

${\sqrt {3}}$

${\frac {2}{\sqrt {3}}}$

$2$

$150^{\circ }$ 
${\frac {5\pi }{6}}$

$225^{\circ }$ 
${\frac {5\pi }{4}}$

${\frac {1}{\sqrt {2}}}$

$1$

${\sqrt {2}}$

$135^{\circ }$ 
${\frac {3\pi }{4}}$

$240^{\circ }$ 
${\frac {4\pi }{3}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{2}}$

${\sqrt {3}}$

${\frac {1}{\sqrt {3}}}$

$2$

${\frac {2}{\sqrt {3}}}$

$120^{\circ }$ 
${\frac {2\pi }{3}}$

$247.5^{\circ }$ 
${\frac {11\pi }{8}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\sqrt {2}}+1$

${\sqrt {2}}1$

${\sqrt {4+2{\sqrt {2}}}}$

${\sqrt {42{\sqrt {2}}}}$

$112.5^{\circ }$ 
${\frac {5\pi }{8}}$

$255^{\circ }$ 
${\frac {17\pi }{12}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

$2+{\sqrt {3}}$

$2{\sqrt {3}}$

${\sqrt {6}}{\sqrt {2}}$

${\sqrt {6}}+{\sqrt {2}}$

$105^{\circ }$ 
${\frac {7\pi }{12}}$

$270^{\circ }$ 
${\frac {3\pi }{2}}$

$1$

$0$

not defined

$0$

not defined

$1$

$90^{\circ }$ 
${\frac {\pi }{2}}$

$285^{\circ }$ 
${\frac {19\pi }{12}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

$2{\sqrt {3}}$

$2+{\sqrt {3}}$

${\sqrt {6}}+{\sqrt {2}}$

${\sqrt {6}}+{\sqrt {2}}$

$75^{\circ }$ 
${\frac {5\pi }{12}}$

$292.5^{\circ }$ 
${\frac {11\pi }{8}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\sqrt {2}}1$

${\sqrt {2}}+1$

${\sqrt {4+2{\sqrt {2}}}}$

${\sqrt {42{\sqrt {2}}}}$

$67.5^{\circ }$ 
${\frac {3\pi }{8}}$

$300^{\circ }$ 
${\frac {5\pi }{3}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{2}}$

${\sqrt {3}}$

${\frac {1}{\sqrt {3}}}$

$2$

${\frac {2}{\sqrt {3}}}$

$60^{\circ }$ 
${\frac {\pi }{3}}$

$315^{\circ }$ 
${\frac {7\pi }{4}}$

${\frac {1}{\sqrt {2}}}$

${\frac {1}{\sqrt {2}}}$

$1$

${\sqrt {2}}$

${\sqrt {2}}$

$45^{\circ }$ 
${\frac {\pi }{4}}$

$330^{\circ }$ 
${\frac {11\pi }{6}}$

${\frac {1}{2}}$

${\frac {\sqrt {3}}{2}}$

${\frac {1}{\sqrt {3}}}$

${\sqrt {3}}$

${\frac {2}{\sqrt {3}}}$

$2$

$30^{\circ }$ 
${\frac {\pi }{6}}$

$337.5^{\circ }$ 
${\frac {15\pi }{8}}$

${\frac {\sqrt {2{\sqrt {2}}}}{2}}$

${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$

${\sqrt {2}}+1$

${\sqrt {2}}1$

${\sqrt {42{\sqrt {2}}}}$

${\sqrt {4+2{\sqrt {2}}}}$

$22.5^{\circ }$ 
${\frac {\pi }{8}}$

$345^{\circ }$ 
${\frac {13\pi }{12}}$

${\frac {{\sqrt {6}}{\sqrt {2}}}{4}}$

${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$

$2+{\sqrt {3}}$

$2{\sqrt {3}}$

${\sqrt {6}}{\sqrt {2}}$

${\sqrt {6}}{\sqrt {2}}$

$15^{\circ }$ 
${\frac {\pi }{12}}$

$360^{\circ }$ 
$2\pi$

$0$

$1$

$0$

not defined

$1$

not defined

$0^{\circ }$ 
$0$
