# Trigonometry/Functions

- See also
**Trigonometry/Polar**for an approach that is useful for -∞<θ<∞

## Fundamental trigonometry functions edit

There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.

## Sine edit

- Sine θ is the length of the leg opposite θ over the length of the hypotenuse:

## Cosine edit

- Cosine θ is the length of the leg adjacent to θ over the hypotenuse:

## Tangent edit

- Tangent of θ is the length of the leg on the opposite side of the triangle from the angle θ over the length of the leg of the triangle adjacent to the angle θ:

These three can be memorized by use of the name of the princess "Soh Cah Toa," meaning:

- "
**s**ine-**o**pposite-**h**ypotenuse **c**osine-**a**djacent-**h**ypotenuse**t**angent-**o**pposite-**a**djacent".

The remaining ratios are reciprocals of the previous ratios:

## Cotangent edit

- Cotangent θ is the reciprocal of tangent θ:

## Secant edit

- Secant θ is the reciprocal of cosine θ:

## Cosecant edit

- Cosecant θ is the reciprocal of sine θ:

## Other considerations edit

- Since the hypotenuse of a right triangle is always the longest side, and
- If we divide both sides of each of these inequalities by the positive number , we get and

or and

## Table edit

### Angle values edit

θ | radians | sinθ | cosθ | tanθ | cotθ | secθ | cosecθ |
---|---|---|---|---|---|---|---|

0° | 0 | 0 | 1 | 0 | undefined | 1 | undefined |

30° | π/6 | 1/2 | 2 | ||||

45° | π/4 | 1 | 1 | ||||

60° | π/3 | 1/2 | 2 | ||||

90° | π/2 | 1 | 0 | undefined | 0 | undefined | 1 |

180° | π | 0 | -1 | 0 | undefined | -1 | undefined |

270° | 3π/2 | -1 | 0 | undefined | 0 | undefined | -1 |

360° | 2π | 0 | 1 | 0 | undefined | 1 | undefined |

## Quiz edit

## Other resources edit

**Reading**: w:Trigonometric_Functions (Wikipedia)**Videos**:

- Basic Trigonometry (Youtube)
- Basic Trigonometry II (Youtube)