Question

Sketch the graph for $y={\sec }^{-1}\left(\sec x\right)$

Answer 1

As $y={\sec }^{-1}\left(\sec x\right)$ is periodic with period $2\pi$
$\therefore$ to draw this graph we should draw the graph for one interval of length $2\pi$ and repeat for entire values of $x$
As we know;
$y={\sec }^{-1}\left(\sec x\right)=\{\begin{array}{c}x;x\in [0,\frac{\pi }{2})\cup (\frac{\pi }{2},\pi ]\\ 2\pi -x;2\pi -x\in [0,\frac{\pi }{2})\cup (\frac{\pi }{2},\pi ]\end{array}$
$=\{\begin{array}{c}x;0\le x<\frac{\pi }{2}\\ 2\pi -x;\pi \le x<\frac{3\pi }{2}\end{array}$