how to graph reciprocal trig functions

worked example: graph $y=2\csc (\frac{\pi }{2}-\frac{\pi }{4})-2$
mean: y=-2
amplitude: 2
period: $4\pi$

worked example: graph $y=\sqrt{3}\cot (\frac{x}{2}+\frac{\pi }{4})-1$
$y=\sqrt{3}\cot \left(\frac{1}{2}(x+\frac{\pi }{2})\right)-1$
mean: y=-1
amplitude: $\sqrt{3}$
period: $2\pi$
start: solve for $\frac{1}{2}(x+\frac{\pi }{2})=0$ to get $x=\frac{\pi }{2}$

worked example:

how to graph inverse trig functions