$\theta$ *(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 |
$-360^{\circ }$ |
$-2\pi$ |
---|

$15^{\circ }$ |
${\frac {\pi }{12}}$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$2-{\sqrt {3}}$ |
$2+{\sqrt {3}}$ |
${\sqrt {6}}-{\sqrt {2}}$ |
${\sqrt {6}}+{\sqrt {2}}$ |
$-345^{\circ }$ |
$-{\frac {13\pi }{12}}$ |
---|

$22.5^{\circ }$ |
${\frac {\pi }{8}}$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
${\sqrt {2}}-1$ |
${\sqrt {2}}+1$ |
${\sqrt {4-2{\sqrt {2}}}}$ |
${\sqrt {4+2{\sqrt {2}}}}$ |
$-337.5^{\circ }$ |
$-{\frac {15\pi }{8}}$ |
---|

$30^{\circ }$ |
${\frac {\pi }{6}}$ |
${\frac {1}{2}}$ |
${\frac {\sqrt {3}}{2}}$ |
${\frac {1}{\sqrt {3}}}$ |
${\sqrt {3}}$ |
${\frac {2}{\sqrt {3}}}$ |
$2$ |
$-330^{\circ }$ |
$-{\frac {11\pi }{6}}$ |
---|

$45^{\circ }$ |
${\frac {\pi }{4}}$ |
${\frac {1}{\sqrt {2}}}$ |
$1$ |
${\sqrt {2}}$ |
$-315^{\circ }$ |
$-{\frac {7\pi }{4}}$ |
---|

$60^{\circ }$ |
${\frac {\pi }{3}}$ |
${\frac {\sqrt {3}}{2}}$ |
${\frac {1}{2}}$ |
${\sqrt {3}}$ |
${\frac {1}{\sqrt {3}}}$ |
$2$ |
${\frac {2}{\sqrt {3}}}$ |
$-300^{\circ }$ |
$-{\frac {5\pi }{3}}$ |
---|

$67.5^{\circ }$ |
${\frac {3\pi }{8}}$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
${\sqrt {2}}+1$ |
${\sqrt {2}}-1$ |
${\sqrt {4+2{\sqrt {2}}}}$ |
${\sqrt {4-2{\sqrt {2}}}}$ |
$-292.5^{\circ }$ |
$-{\frac {11\pi }{8}}$ |
---|

$75^{\circ }$ |
${\frac {5\pi }{12}}$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$2+{\sqrt {3}}$ |
$2-{\sqrt {3}}$ |
${\sqrt {6}}+{\sqrt {2}}$ |
${\sqrt {6}}-{\sqrt {2}}$ |
$-285^{\circ }$ |
$-{\frac {19\pi }{12}}$ |
---|

$90^{\circ }$ |
${\frac {\pi }{2}}$ |
$1$ |
$0$ |
*not*
defined |
$0$ |
*not*
defined |
$1$ |
$-270^{\circ }$ |
$-{\frac {3\pi }{2}}$ |
---|

$105^{\circ }$ |
${\frac {7\pi }{12}}$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$-2-{\sqrt {3}}$ |
$-2+{\sqrt {3}}$ |
$-{\sqrt {6}}-{\sqrt {2}}$ |
${\sqrt {6}}-{\sqrt {2}}$ |
$-255^{\circ }$ |
$-{\frac {17\pi }{12}}$ |
---|

$112.5^{\circ }$ |
${\frac {5\pi }{8}}$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
$-{\sqrt {2}}-1$ |
$-{\sqrt {2}}+1$ |
$-{\sqrt {4+2{\sqrt {2}}}}$ |
${\sqrt {4-2{\sqrt {2}}}}$ |
$-247.5^{\circ }$ |
$-{\frac {11\pi }{8}}$ |
---|

$120^{\circ }$ |
${\frac {2\pi }{3}}$ |
${\frac {\sqrt {3}}{2}}$ |
$-{\frac {1}{2}}$ |
$-{\sqrt {3}}$ |
$-{\frac {1}{\sqrt {3}}}$ |
$-2$ |
${\frac {2}{\sqrt {3}}}$ |
$-240^{\circ }$ |
$-{\frac {4\pi }{3}}$ |
---|

$135^{\circ }$ |
${\frac {3\pi }{4}}$ |
${\frac {1}{\sqrt {2}}}$ |
$-{\frac {1}{\sqrt {2}}}$ |
$-1$ |
$-{\sqrt {2}}$ |
${\sqrt {2}}$ |
$-225^{\circ }$ |
$-{\frac {5\pi }{4}}$ |
---|

$150^{\circ }$ |
${\frac {5\pi }{6}}$ |
${\frac {1}{2}}$ |
$-{\frac {\sqrt {3}}{2}}$ |
$-{\frac {1}{\sqrt {3}}}$ |
$-{\sqrt {3}}$ |
$-{\frac {2}{\sqrt {3}}}$ |
$2$ |
$-210^{\circ }$ |
$-{\frac {7\pi }{6}}$ |
---|

$157.5^{\circ }$ |
${\frac {7\pi }{8}}$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
$-{\sqrt {2}}+1$ |
$-{\sqrt {2}}-1$ |
$-{\sqrt {4-2{\sqrt {2}}}}$ |
${\sqrt {4+2{\sqrt {2}}}}$ |
$-202.5^{\circ }$ |
$-{\frac {9\pi }{8}}$ |
---|

$165^{\circ }$ |
${\frac {11\pi }{12}}$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$-2+{\sqrt {3}}$ |
$-2-{\sqrt {3}}$ |
$-{\sqrt {6}}+{\sqrt {2}}$ |
${\sqrt {6}}+{\sqrt {2}}$ |
$-195^{\circ }$ |
$-{\frac {13\pi }{12}}$ |
---|

$180^{\circ }$ |
$\pi$ |
$0$ |
$-1$ |
$0$ |
*not*
defined |
$-1$ |
*not*
defined |
$-180^{\circ }$ |
$-\pi$ |
---|

$195^{\circ }$ |
${\frac {13\pi }{12}}$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$2-{\sqrt {3}}$ |
$2+{\sqrt {3}}$ |
$-{\sqrt {6}}+{\sqrt {2}}$ |
$-{\sqrt {6}}-{\sqrt {2}}$ |
$-165^{\circ }$ |
$-{\frac {11\pi }{12}}$ |
---|

$202.5^{\circ }$ |
${\frac {9\pi }{8}}$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
${\sqrt {2}}-1$ |
${\sqrt {2}}+1$ |
$-{\sqrt {4-2{\sqrt {2}}}}$ |
$-{\sqrt {4+2{\sqrt {2}}}}$ |
$-157.5^{\circ }$ |
$-{\frac {7\pi }{8}}$ |
---|

$210^{\circ }$ |
${\frac {7\pi }{6}}$ |
$-{\frac {1}{2}}$ |
$-{\frac {\sqrt {3}}{2}}$ |
${\frac {1}{\sqrt {3}}}$ |
${\sqrt {3}}$ |
$-{\frac {2}{\sqrt {3}}}$ |
$-2$ |
$-150^{\circ }$ |
$-{\frac {5\pi }{6}}$ |
---|

$225^{\circ }$ |
${\frac {5\pi }{4}}$ |
$-{\frac {1}{\sqrt {2}}}$ |
$1$ |
$-{\sqrt {2}}$ |
$-135^{\circ }$ |
$-{\frac {3\pi }{4}}$ |
---|

$240^{\circ }$ |
${\frac {4\pi }{3}}$ |
$-{\frac {\sqrt {3}}{2}}$ |
$-{\frac {1}{2}}$ |
${\sqrt {3}}$ |
${\frac {1}{\sqrt {3}}}$ |
$-2$ |
$-{\frac {2}{\sqrt {3}}}$ |
$-120^{\circ }$ |
$-{\frac {2\pi }{3}}$ |
---|

$247.5^{\circ }$ |
${\frac {11\pi }{8}}$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
${\sqrt {2}}+1$ |
${\sqrt {2}}-1$ |
$-{\sqrt {4+2{\sqrt {2}}}}$ |
$-{\sqrt {4-2{\sqrt {2}}}}$ |
$-112.5^{\circ }$ |
$-{\frac {5\pi }{8}}$ |
---|

$255^{\circ }$ |
${\frac {17\pi }{12}}$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$2+{\sqrt {3}}$ |
$2-{\sqrt {3}}$ |
$-{\sqrt {6}}-{\sqrt {2}}$ |
$-{\sqrt {6}}+{\sqrt {2}}$ |
$-105^{\circ }$ |
$-{\frac {7\pi }{12}}$ |
---|

$270^{\circ }$ |
${\frac {3\pi }{2}}$ |
$-1$ |
$0$ |
*not*
defined |
$0$ |
*not*
defined |
$-1$ |
$-90^{\circ }$ |
$-{\frac {\pi }{2}}$ |
---|

$285^{\circ }$ |
${\frac {19\pi }{12}}$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
$-2-{\sqrt {3}}$ |
$-2+{\sqrt {3}}$ |
${\sqrt {6}}+{\sqrt {2}}$ |
$-{\sqrt {6}}+{\sqrt {2}}$ |
$-75^{\circ }$ |
$-{\frac {5\pi }{12}}$ |
---|

$292.5^{\circ }$ |
${\frac {11\pi }{8}}$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
$-{\sqrt {2}}-1$ |
$-{\sqrt {2}}+1$ |
${\sqrt {4+2{\sqrt {2}}}}$ |
$-{\sqrt {4-2{\sqrt {2}}}}$ |
$-67.5^{\circ }$ |
$-{\frac {3\pi }{8}}$ |
---|

$300^{\circ }$ |
${\frac {5\pi }{3}}$ |
$-{\frac {\sqrt {3}}{2}}$ |
${\frac {1}{2}}$ |
$-{\sqrt {3}}$ |
$-{\frac {1}{\sqrt {3}}}$ |
$2$ |
$-{\frac {2}{\sqrt {3}}}$ |
$-60^{\circ }$ |
$-{\frac {\pi }{3}}$ |
---|

$315^{\circ }$ |
${\frac {7\pi }{4}}$ |
$-{\frac {1}{\sqrt {2}}}$ |
${\frac {1}{\sqrt {2}}}$ |
$-1$ |
${\sqrt {2}}$ |
$-{\sqrt {2}}$ |
$-45^{\circ }$ |
$-{\frac {\pi }{4}}$ |
---|

$330^{\circ }$ |
${\frac {11\pi }{6}}$ |
$-{\frac {1}{2}}$ |
${\frac {\sqrt {3}}{2}}$ |
$-{\frac {1}{\sqrt {3}}}$ |
$-{\sqrt {3}}$ |
${\frac {2}{\sqrt {3}}}$ |
$-2$ |
$-30^{\circ }$ |
$-{\frac {\pi }{6}}$ |
---|

$337.5^{\circ }$ |
${\frac {15\pi }{8}}$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$ |
$-{\sqrt {2}}+1$ |
$-{\sqrt {2}}-1$ |
${\sqrt {4-2{\sqrt {2}}}}$ |
$-{\sqrt {4+2{\sqrt {2}}}}$ |
$-22.5^{\circ }$ |
$-{\frac {\pi }{8}}$ |
---|

$345^{\circ }$ |
${\frac {13\pi }{12}}$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}$ |
$-2+{\sqrt {3}}$ |
$-2-{\sqrt {3}}$ |
${\sqrt {6}}-{\sqrt {2}}$ |
$-{\sqrt {6}}-{\sqrt {2}}$ |
$-15^{\circ }$ |
$-{\frac {\pi }{12}}$ |
---|

$360^{\circ }$ |
$2\pi$ |
$0$ |
$1$ |
$0$ |
*not*
defined |
$1$ |
*not*
defined |
$0^{\circ }$ |
$0$ |
---|