Question

How do you graph to solve the equation on the interval `[-2pi,2pi]` for `cscx=-(2sqrt3)/3`?

Answer 1

`-pi/3, (-2pi)/3, (4pi)/3, (5pi)/3`

Explanation:

`csc x = 1/(sin x) = - (2sqrt3)/3`
`sin x = - 3/(2sqrt3) = - sqrt3/2`
Use trig table of special arcs and unit circle:

For interval `(- 2pi, 0)`, there are 2 answers:
`sin x = - sqrt3/2` --> `x = - pi/3` and `x = (-2pi)/3`
For interval `(0, 2pi)`, there are 2 answers:
sin x = - sqrt3.2 ---> `x = (4pi)/3` and `x = (5pi)/3`