Solve sin4 theta 12 for the first 4 solution of theta in t

Solve sin(4 theta) = - 1/2 for the first 4 solution of theta in the interval [0,2pi) Enter your answer in exact form and in ascending order.

Solution

sin4theta = -1/2

interval [ 0, 2pi]

4theta = sin^-1(-1/2)

4theta = pi+pi/6 , 2pi -pi/6

4theta = 7pi/6

General solution : theta = (2pi*k +7pi/6)/4

General solution : theta = (2pi*k + 11pi/6)/4

First four solutuions: theta = 7pi/24 , 11pi/24 , 19pi/24 ,23pi/24