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

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).

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

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