# Trigonometric Ratio

## Definition

The ratio of lengths of any two of three sides of a right angled triangle at an angle is called trigonometric ratio.

A right angled triangle contains three sides and a ratio is calculated by taking lengths of any two sides from three sides.

For example:

$$\frac{Length \, of \, Opposite \, side}{Length \, of \, Hypotenuse}$$

The possible ratios of three sides in a triangle by taking two sides each, are $3!$ which means $6$ ratios are possible.

### List of Ratios

Each trigonometric ratio is represented by a name to avoid complexity in expressing the ratios in terms of lengths of any two sides. Here is the list of $6$ trigonometric ratios and their definitions with represented names.

1

#### Sine

The ratio of length of opposite side to length of hypotenuse at an angle of right angled triangle is called sine.
2

#### Cosine

The ratio of length of adjacent side to length of hypotenuse at an angle of right angled triangle is called cosine.
3

#### Tangent

The ratio of length of opposite side to length of adjacent side at an angle of right angled triangle is called tangent.
4

#### Cotangent

The ratio of length of adjacent side to length of opposite side at an angle of right angled triangle is called cotangent.
5

#### Secant

The ratio of length of hypotenuse to length of adjacent side at an angle of right angled triangle is called secant.
6

#### Cosecant

The ratio of length of hypotenuse to length of opposite side at an angle of right angled triangle is called cosecant.