Question

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

Answer 1

As, $y={\cot }^{-1}\left(\cot x\right)$ is periodic with period $\pi$
$\therefore$ to draw this graph we should draw the graph for one interval of length $\pi$ and repeat for entire values of $x$
As we know $y={\cot }^{-1}\left(\cot x\right)=\{x:0<x<\pi \}$
which is defined for length $\pi$ i.e., $x\in (0,\pi )$ and $x\notin \{n\pi ;n\in Z\}$
So, its graph could be plotted as;