Question

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

Answer 1

See below.

Explanation:

Since you will be graphing `y=csc(x)` this is the same as `y=1/cosx`

Notice from the graph that the vertical lines are asymptotes. This is because `y=1/cosx` is undefined anywhere `cosx=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 `cscx=sqrt(2)`. It's very difficult to get accurate solutions from a graph though.