# Secant

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

## Introduction

Secant is a name and it is introduced in trigonometry to represent the ratio of lengths of hypotenuse to adjacent side at a particular angle in a right angled triangle. It is usually written in ratio form and alternatively as secant with angle.

#### 1. Ratio

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

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

Hence, secant is called generally as a trigonometric ratio.

#### 2. Function

Mathematically, the value of secant at an angle is written in alternate way by just writing secant in its short form $\sec$ and then respective angle of the right triangle.

For example, if angle of a right triangle is represented by $x$, then secant of angle $x$ is written as $\sec{x}$ in trigonometry and the $\sec{x}$ is a function form. Hence, it is generally called as secant function in mathematics.

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

### Mathematical form

$\Delta BAC$ is a right triangle and angle of this triangle is denoted by theta ($\theta$). secant of angle is written as $\sec{\theta}$ in this case.

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

It is actually used as a formula to calculate the value of secant at any angle of the right triangle.

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

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

#### Values

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

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