Calculate csc(45)°

Since our angle is between 0 and 90 degrees, it is located in Quadrant I

In the first quadrant, the values for sin, cos and tan are positive.

45 is an acute angle since it is less than 90°

Csc(θ) = | 1 |

Sin(θ) |

csc(45) = | 1 |

Sin(45) |

csc(45) = | 1 |

Sin(√2/2) |

csc(45) = √2

Since 45° is less than 90, we can express this in terms of a cofunction

(θ) = (90 - θ) = (90 - 45) = (45)

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 |