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

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.

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.

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.

$\Delta BAC$ 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).

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

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

Latest Math Topics

Nov 11, 2022

Nov 03, 2022

Jul 24, 2022

Jul 15, 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