# How do you find the amplitude and period of Arc Sec?

Jul 5, 2015

arcsec does not have a (meaningful) amplitude or period.
You seem to have confused arcsec with the direct trigonometric functions

#### Explanation:

arcsec(x) is an angle; typically its value is restricted to angles in the range $\left[0 , 2 \pi\right)$

In terms of a unit circle arcsec(x) is the angle $\theta$ such that the hypotenuse divided by the adjacent side of a unit circle triangle based at the origin has the ratio $x$.
Since the hypotenuse must be at least as long as any other side $x$ is undefined for any value in the range $\left(- 1 , + 1\right)$

The graph below demonstrates the arcsin relationship.
The vertical axis is the angle (in radians).
The horizontal axis is the arcsin argument value.

graph{x=sec(y) [-14.24, 14.23, -7.11, 7.13]}