Calculate csc(120)°

Since our angle is greater than 90 and less than or equal to 180 degrees, it is located in Quadrant II

In the second quadrant, the values for sin are positive only.

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

Csc(θ) = | 1 |

Sin(θ) |

csc(120) = | 1 |

Sin(120) |

csc(120) = | 1 |

Sin(√3/2) |

csc(120) = 2√33

Since 120° is less than 90, we can express this in terms of a cofunction

(θ) = (90 - θ) = (90 - 120) = (-30)

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 |