Math Doubts

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 ($\theta$).

right angled triangle

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.

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



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