trigonometric functions

Question

Find the solutions of the equation in the interval [−2𝜋, 2𝜋]. Use a graphing utility to verify your results. (Enter your answers as a comma-separated list.)

csc(x) = 2

Answer 1

cscx = 2 = 1/sinx, sinx = 1/2, reference angle is 30 degrees = pi/6. It's a 1-sqr3-2 right triangle. Hypotenuse =2, opposite side = 1. sinx and cscx are positive only in quadrants I and II.

x = pi/6, 5pi/6, - 7pi/6 or - 11pi/6

or 30, 150, -330 or -210 degrees