Sin^2 x-1/4=0 find exact solution over the interval [0,2pi)

sin² (x) - 0.25 = 0

sin² (x) + 0.5sin (x) - 0.5sin (x) - 0.25 = 0

sin (x) [sin (x) ] + sin (x) [0.5] - 0.5[sin (x) ] - 0.5[0.5] = 0

sin (x) [sin (x) + 0.5] - 0.5[sin (x) + 0.5] = 0

[sin (x) - 0.5][sin (x) + 0.5] = 0

sin (x) - 0.5 = 0 or sin (x) + 0.5 = 0

sin (x) = 0.5 sin (x) = - 0.5

sin⁻¹[sin (x) ] = sin⁻¹ (0.5) sin⁻¹[sin (x) ] = sin⁻¹ (-0.5)

x = 30°, ¹/₆π radians x = 210°, 1¹/₆π radians

150°, ⁵/₆π radians 330°, 1⁵/₆π radians