# How do you graph y=-2csc(2x)+1?

Nov 18, 2016

Using the Socratic graphic facility, I have inserted a graph.

#### Explanation:

The period of y is $\frac{2 \pi}{2} = \pi$. It is convenient to choose one

period as #x in (-pi/2, pi/2). Note that y has infinite discontinuity at

the ends and the middle x = 0.

A Table for making the graph:

$\left(x , y\right) : \left(3.31 , - \frac{\pi}{3}\right) \left(3 , - \frac{\pi}{4}\right) \left(3.1 , - \frac{\pi}{6}\right) \left(\infty , 0\right)$

$\left(- 1.3 , \frac{\pi}{6}\right) \left(- 1 , \frac{\pi}{4}\right) \left(- 1.3 , \frac{\pi}{3}\right)$

The part of the inserted graph that braces the y-axis is the graph for

this period.

ygraph{(y-1) sin (2x)+2=0 [-9.91, 10.09, -3.68, 6.32]}