Question

Find all the roots of the equation Sin(2x)=1/2 in the range of -pi<x<pi giving answers in radians as multiples of Pi

Answer 1

sin 2x = 1/2
so 2x = π/6 or 2x = 5π/6 , (30° or 150°
x = π/12 or x = 5π/12 , (15° or 75°)

the period of sin 2x is π , (180°)
so adding or subtracting π to any answer will produce another answer.

but adding π to our positive answers will send us beyond our domain, so let's subtract

x = π/12 - π = -11π/12 , (-165°) or
x = 5π/12 - π = -7π/12 , (-105°)

so for your given domain
x = -11π,12, -7π/12, π/12, 5π/12