Solution of Trignometric Equation in Radians

Topic : Trignometric Equations

Question : Determine all solutions of each equation in radians in the interval (0,2 π)
4 Sin² x - 1 = 0

Solution :
4 Sin² x - 1 = 0
4 Sin² x = 1
Sin² x = 1/4
Sin x = √(1/4)
Sin x = ± 1/2

If Sin x = + 1/2
Sin x = Sin π/6
x = π/6
and
Sin x = Sin (π - π/6)
x = 5π/6

If Sin x = - 1/2
Sin x = Sin (π + π/6)
x = 7π/6
and
Sin x = Sin (2π - π/6)
x = 11π/6

Therefore the Answer is {π/6, 5π/6, 7π/6, 11π/6}