# Cosine

The relation between angle and ratio of lengths of adjacent side to hypotenuse in a right triangle is called cosine.

## Introduction

Cosine is a name and it actually represents the ratio of lengths of adjacent side to hypotenuse at a particular angle in a right triangle. It can be written in ratio form and also as cosine with angle alternatively.

#### 1. Ratio

The value of cosine at an angle is calculated by the ratio of lengths of adjacent side to hypotenuse.

$\dfrac{Length \, of \, Adjacent \, side}{Length \, of \, Hypotenuse}$

Hence, cosine is called as a trigonometric ratio in general.

#### 2. Function

Alternatively, the value of cosine at an angle is written mathematically by writing cosine in its short form $\cos$ and then respective angle of the right angled triangle.

For example, if angle of right triangle is represented by $x$, then cosine of angle $x$ is written as $\cos{x}$ in trigonometry. $\cos{x}$ is a function form. Therefore, it is usually called as cos function in mathematics.

Thus, cos functions like $\cos{A}$, $\cos{\alpha}$, $\cos{\beta}$, and etc. are defined in mathematics.

### Mathematical form

$\Delta CAB$ is a right triangle and its angle is denoted by theta ($\theta$).

cosine of angle is written as $\cos{\theta}$ in this case.

$\cos{\theta} \,=\, \dfrac{Length \, of \, Adjacent \, side}{Length \, of \, Hypotenuse}$

It can be used as a formula to calculate the value of cosine at any angle of the right triangle.

In this example, $AB$ is length of adjacent side (base) and $AC$ is length of hypotenuse.

$\,\,\, \therefore \,\,\,\,\,\, \cos{\theta} \,=\, \dfrac{AB}{AC}$