$\theta \,$ *(positive)* |
$\sin \theta \,$ |
$\cos \theta \,$ |
$\tan \theta \,$ |
$\cot \theta \,$ |
$\sec \theta \,$ |
$\csc \theta \,$ |
$\theta \,$ *(negative)* |
---|

*(degrees)* |
*(radians)* |
*(degrees)* |
*(radians)* |
---|

0° |
$0\,$ |
$0\,$ |
$1\,$ |
$0\,$ |
*not*
defined |
$1\,$ |
*not*
defined |
−360° |
$-2\pi \,$ |
---|

15° |
${\frac {\pi }{12}}\,$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$2-{\sqrt {3}}\,$ |
$2+{\sqrt {3}}\,$ |
${\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
${\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
−345° |
$-{\frac {13\pi }{12}}\,$ |
---|

22.5° |
${\frac {\pi }{8}}\,$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
${\sqrt {2}}-1\,$ |
${\sqrt {2}}+1\,$ |
${\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
${\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
−337.5° |
$-{\frac {15\pi }{8}}\,$ |
---|

30° |
${\frac {\pi }{6}}\,$ |
${\frac {1}{2}}\,$ |
${\frac {\sqrt {3}}{2}}\,$ |
${\frac {1}{\sqrt {3}}}\,$ |
${\sqrt {3}}\,$ |
${\frac {2}{\sqrt {3}}}\,$ |
$2\,$ |
−330° |
$-{\frac {11\pi }{6}}\,$ |
---|

45° |
${\frac {\pi }{4}}\,$ |
${\frac {1}{\sqrt {2}}}\,$ |
${\frac {1}{\sqrt {2}}}\,$ |
$1\,$ |
$1\,$ |
${\sqrt {2}}\,$ |
${\sqrt {2}}\,$ |
−315° |
$-{\frac {7\pi }{4}}\,$ |
---|

60° |
${\frac {\pi }{3}}\,$ |
${\frac {\sqrt {3}}{2}}\,$ |
${\frac {1}{2}}\,$ |
${\sqrt {3}}\,$ |
${\frac {1}{\sqrt {3}}}\,$ |
$2\,$ |
${\frac {2}{\sqrt {3}}}\,$ |
−300° |
$-{\frac {5\pi }{3}}\,$ |
---|

67.5° |
${\frac {3\pi }{8}}\,$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
${\sqrt {2}}+1\,$ |
${\sqrt {2}}-1\,$ |
${\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
${\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
−292.5° |
$-{\frac {11\pi }{8}}\,$ |
---|

75° |
${\frac {5\pi }{12}}\,$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$2+{\sqrt {3}}\,$ |
$2-{\sqrt {3}}\,$ |
${\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
${\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
−285° |
$-{\frac {19\pi }{12}}\,$ |
---|

90° |
${\frac {\pi }{2}}\,$ |
$1\,$ |
$0\,$ |
*not*
defined |
$0\,$ |
*not*
defined |
$1\,$ |
−270° |
$-{\frac {3\pi }{2}}\,$ |
---|

105° |
${\frac {7\pi }{12}}\,$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$-2-{\sqrt {3}}\,$ |
$-2+{\sqrt {3}}\,$ |
$-{\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
${\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
−255° |
$-{\frac {17\pi }{12}}\,$ |
---|

112.5° |
${\frac {5\pi }{8}}\,$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
$-{\sqrt {2}}-1\,$ |
$-{\sqrt {2}}+1\,$ |
$-{\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
${\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
−247.5° |
$-{\frac {11\pi }{8}}\,$ |
---|

120° |
${\frac {2\pi }{3}}\,$ |
${\frac {\sqrt {3}}{2}}\,$ |
$-{\frac {1}{2}}\,$ |
$-{\sqrt {3}}\,$ |
$-{\frac {1}{\sqrt {3}}}\,$ |
$-2\,$ |
${\frac {2}{\sqrt {3}}}\,$ |
−240° |
$-{\frac {4\pi }{3}}\,$ |
---|

135° |
${\frac {3\pi }{4}}\,$ |
${\frac {1}{\sqrt {2}}}\,$ |
$-{\frac {1}{\sqrt {2}}}\,$ |
$-1\,$ |
$-1\,$ |
$-{\sqrt {2}}\,$ |
${\sqrt {2}}\,$ |
−225° |
$-{\frac {5\pi }{4}}\,$ |
---|

150° |
${\frac {5\pi }{6}}\,$ |
${\frac {1}{2}}\,$ |
$-{\frac {\sqrt {3}}{2}}\,$ |
$-{\frac {1}{\sqrt {3}}}\,$ |
$-{\sqrt {3}}\,$ |
$-{\frac {2}{\sqrt {3}}}\,$ |
$2\,$ |
−210° |
$-{\frac {7\pi }{6}}\,$ |
---|

157.5° |
${\frac {7\pi }{8}}\,$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
$-{\sqrt {2}}+1\,$ |
$-{\sqrt {2}}-1\,$ |
$-{\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
${\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
−202.5° |
$-{\frac {9\pi }{8}}\,$ |
---|

165° |
${\frac {11\pi }{12}}\,$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$-2+{\sqrt {3}}\,$ |
$-2-{\sqrt {3}}\,$ |
$-{\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
${\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
−195° |
$-{\frac {13\pi }{12}}\,$ |
---|

180° |
$\pi \,$ |
$0\,$ |
$-1\,$ |
$0\,$ |
*not*
defined |
$-1\,$ |
*not*
defined |
−180° |
$-\pi \,$ |
---|

195° |
${\frac {13\pi }{12}}\,$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$2-{\sqrt {3}}\,$ |
$2+{\sqrt {3}}\,$ |
$-{\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
$-{\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
−165° |
$-{\frac {11\pi }{12}}\,$ |
---|

202.5° |
${\frac {9\pi }{8}}\,$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
${\sqrt {2}}-1\,$ |
${\sqrt {2}}+1\,$ |
$-{\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
$-{\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
−157.5° |
$-{\frac {7\pi }{8}}\,$ |
---|

210° |
${\frac {7\pi }{6}}\,$ |
$-{\frac {1}{2}}\,$ |
$-{\frac {\sqrt {3}}{2}}\,$ |
${\frac {1}{\sqrt {3}}}\,$ |
${\sqrt {3}}\,$ |
$-{\frac {2}{\sqrt {3}}}\,$ |
$-2\,$ |
−150° |
$-{\frac {5\pi }{6}}\,$ |
---|

225° |
${\frac {5\pi }{4}}\,$ |
$-{\frac {1}{\sqrt {2}}}\,$ |
$-{\frac {1}{\sqrt {2}}}\,$ |
$1\,$ |
$1\,$ |
$-{\sqrt {2}}\,$ |
$-{\sqrt {2}}\,$ |
−135° |
$-{\frac {3\pi }{4}}\,$ |
---|

240° |
${\frac {4\pi }{3}}\,$ |
$-{\frac {\sqrt {3}}{2}}\,$ |
$-{\frac {1}{2}}\,$ |
${\sqrt {3}}\,$ |
${\frac {1}{\sqrt {3}}}\,$ |
$-2\,$ |
$-{\frac {2}{\sqrt {3}}}\,$ |
−120° |
$-{\frac {2\pi }{3}}\,$ |
---|

247.5° |
${\frac {11\pi }{8}}\,$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
${\sqrt {2}}+1\,$ |
${\sqrt {2}}-1\,$ |
$-{\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
$-{\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
−112.5° |
$-{\frac {5\pi }{8}}\,$ |
---|

255° |
${\frac {17\pi }{12}}\,$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$2+{\sqrt {3}}\,$ |
$2-{\sqrt {3}}\,$ |
$-{\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
$-{\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
−105° |
$-{\frac {7\pi }{12}}\,$ |
---|

270° |
${\frac {3\pi }{2}}\,$ |
$-1\,$ |
$0\,$ |
*not*
defined |
$0\,$ |
*not*
defined |
$-1\,$ |
−90° |
$-{\frac {\pi }{2}}\,$ |
---|

285° |
${\frac {19\pi }{12}}\,$ |
$-{\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
${\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
$-2-{\sqrt {3}}\,$ |
$-2+{\sqrt {3}}\,$ |
${\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
$-{\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
−75° |
$-{\frac {5\pi }{12}}\,$ |
---|

292.5° |
${\frac {11\pi }{8}}\,$ |
$-{\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
${\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
$-{\sqrt {2}}-1\,$ |
$-{\sqrt {2}}+1\,$ |
${\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
$-{\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
−67.5° |
$-{\frac {3\pi }{8}}\,$ |
---|

300° |
${\frac {5\pi }{3}}\,$ |
$-{\frac {\sqrt {3}}{2}}\,$ |
${\frac {1}{2}}\,$ |
$-{\sqrt {3}}\,$ |
$-{\frac {1}{\sqrt {3}}}\,$ |
$2\,$ |
$-{\frac {2}{\sqrt {3}}}\,$ |
−60° |
$-{\frac {\pi }{3}}\,$ |
---|

315° |
${\frac {7\pi }{4}}\,$ |
$-{\frac {1}{\sqrt {2}}}\,$ |
${\frac {1}{\sqrt {2}}}\,$ |
$-1\,$ |
$-1\,$ |
${\sqrt {2}}\,$ |
$-{\sqrt {2}}\,$ |
−45° |
$-{\frac {\pi }{4}}\,$ |
---|

330° |
${\frac {11\pi }{6}}\,$ |
$-{\frac {1}{2}}\,$ |
${\frac {\sqrt {3}}{2}}\,$ |
$-{\frac {1}{\sqrt {3}}}\,$ |
$-{\sqrt {3}}\,$ |
${\frac {2}{\sqrt {3}}}\,$ |
$-2\,$ |
−30° |
$-{\frac {\pi }{6}}\,$ |
---|

337.5° |
${\frac {15\pi }{8}}\,$ |
$-{\frac {\sqrt {2-{\sqrt {2}}}}{2}}\,$ |
${\frac {\sqrt {2+{\sqrt {2}}}}{2}}\,$ |
$-{\sqrt {2}}+1\,$ |
$-{\sqrt {2}}-1\,$ |
${\frac {2}{\sqrt {2+{\sqrt {2}}}}}\,$ |
$-{\frac {2}{\sqrt {2-{\sqrt {2}}}}}\,$ |
−22.5° |
$-{\frac {\pi }{8}}\,$ |
---|

345° |
${\frac {13\pi }{12}}\,$ |
$-{\frac {{\sqrt {6}}-{\sqrt {2}}}{4}}\,$ |
${\frac {{\sqrt {6}}+{\sqrt {2}}}{4}}\,$ |
$-2+{\sqrt {3}}\,$ |
$-2-{\sqrt {3}}\,$ |
${\frac {4}{{\sqrt {6}}+{\sqrt {2}}}}\,$ |
$-{\frac {4}{{\sqrt {6}}-{\sqrt {2}}}}\,$ |
−15° |
$-{\frac {\pi }{12}}\,$ |
---|

360° |
$2\pi \,$ |
$0\,$ |
$1\,$ |
$0\,$ |
*not*
defined |
$1\,$ |
*not*
defined |
0° |
$0\,$ |
---|