Find all solutions to the equation squareroot 3 esc theta 2

Find all solutions to the equation. squareroot 3 esc theta + 2 = 0 Write your answer in radians in terms of n, and use the \"or\" button as necessary. Example: theta = pi/5 + 2 k pi, k Z or theta = pi/7 + k pi, k Z

Solution

sqrt 3 csc theta + 2 = 0

subtracting 2 from both sides

sqrt 3 csc theta = -2

dividing both sides by sqrt 3

csc theta = -2 / sqrt 3

theta = csc^-1 ( -2/sqrt 3)

theta = 4pi/3 + 2k*pi , 5pi/3 + 2k*pi