Question

How do you find two solutions (in degree and radians) for `cscx = -sqrt2`?

Answer 1

Solve csc x = -sqrt2

Ans: `(5pi)/4 and (7pi)/4`

Explanation:

`csc x = 1/(sin x) = -sqrt2`. First, find sin x.
Use Trig Table and unit circle -->
`sin x = -1/(sqrt2) = -sqrt2/2` --> `x = - pi/4` and `x = -(3pi)/4`
Answers, using co-terminal arcs:
`x = - (3pi)/4` or `x = (5pi)/4, or 225^@`
`x = -pi/4`, or `x = (7pi)/4, or 315^@`