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

1 answer:

4 0

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

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