Calculate csc(280)°

Since our angle is greater than 270 and less than or equal to 360 degrees, it is located in Quadrant IV

In the fourth quadrant, the values for cos are positive only.

280 is an obtuse angle since it is greater than 90°

Csc(θ) = | 1 |

Sin(θ) |

csc(280) = | 1 |

Sin(280) |

csc(280) = | 1 |

Sin(-0.88) |

csc(280) = -9

Since 280° is less than 90, we can express this in terms of a cofunction

(θ) = (90 - θ) = (90 - 280) = (-190)

θ° | θ^{radians} | sin(θ) | cos(θ) | tan(θ) | csc(θ) | sec(θ) | cot(θ) |
---|---|---|---|---|---|---|---|

0° | 0 | 0 | 1 | 0 | 0 | 1 | 0 |

30° | π/6 | 1/2 | √3/2 | √3/3 | 2 | 2√3/3 | √3 |

45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 |

60° | π/3 | √3/2 | 1/2 | √3 | 2√3/3 | 2 | √3/3 |

90° | π/2 | 1 | 0 | N/A | 1 | 0 | N/A |

120° | 2π/3 | √3/2 | -1/2 | -√3 | 2√3/3 | -2 | -√3/3 |

135° | 3π/4 | √2/2 | -√2/2 | -1 | √2 | -√2 | -1 |

150° | 5π/6 | 1/2 | -√3/2 | -√3/3 | 2 | -2√3/3 | -√3 |

180° | π | 0 | -1 | 0 | 0 | -1 | N/A |

210° | 7π/6 | -1/2 | -√3/2 | √3/3 | -2 | -2√3/3 | -√3 |

225° | 5π/4 | -√2/2 | -√2/2 | 1 | -√2 | -√2 | 1 |

240° | 4π/3 | -√3/2 | -1/2 | -√3 | -2√3/3 | -2 | -√3/3 |

270° | 3π/2 | -1 | 0 | N/A | -1 | 0 | N/A |

300° | 5π/3 | -√3/2 | 1/2 | -√3 | -2√3/3 | 2 | -√3/3 |

315° | 7π/4 | -√2/2 | √2/2 | -1 | -√2 | √2 | -1 |

330° | 11π/6 | -1/2 | √3/2 | -√3/3 | -2 | 2√3/3 | -√3 |