# How do you graph y=csc(pi-x) and include two full periods?

Jul 28, 2018

See graph and details.

#### Explanation:

$y = \csc \left(\pi - x\right) = \frac{1}{\sin} \left(\pi - x\right) = \frac{1}{\sin} x \notin \left(- 1 , 1\right)$

And, asymptotic x = any zero of the denominator $\sin x$

$= k \pi , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

The period = period of $\sin x = 2 \pi$.

Graph for two periods,

$x \in \left(- 2 \pi , 2 \pi\right)$, with asymptotes $x = \pm \pi$ and

y not-to-be-in $\left(- 1 , 1\right)$:
graph{(y sin x - 1)(y^2-1)(x)(x^2-(pi)^2)(x^2-4(pi)^2)=0[-10 10 -5 5]}