A term that represents a ratio of lengths of adjacent side to opposite side at an angle of a right triangle is called the cotangent.

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.

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.

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.

$\Delta CAB$ 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 opposite side (Base) and $AC$ is length of hypotenuse.

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

The list of exact values of cotangent functions in fraction and decimal forms in a table with proofs.

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved