# How do you graph to solve the equation on the interval [-2pi,2pi] for cscx=sqrt2?

Nov 13, 2017

See below.

#### Explanation:

Since you will be graphing $y = \csc \left(x\right)$ this is the same as $y = \frac{1}{\cos} x$

Notice from the graph that the vertical lines are asymptotes. This is because $y = \frac{1}{\cos} x$ is undefined anywhere $\cos x = 0$.

( this results in division by zero ).

Graph the line $y = \sqrt{2}$ on the same plot. Where $y = \sqrt{2}$ cuts the curves, not the asymptotes, are the solutions to $\csc x = \sqrt{2}$. It's very difficult to get accurate solutions from a graph though.