Answer
$a.$
Intercepts: $(-\pi,0),(\pi,0),$ and $(0,0).$
$b.$
Domain: $[-\pi,\pi]$
Range: $[-1,1]$
$c.$
Increases on $[-\displaystyle \frac{\pi}{2},\frac{\pi}{2}]$
Decreases on: $[-\displaystyle \pi,-\frac{\pi}{2}]$ and $[\displaystyle \frac{\pi}{2},\pi]$
$d.$
The graph has origin symmetry, so the function is odd.
Work Step by Step
See image(s).