Mathematics
jes12
18

Find all values of x in the interval [0, 2π] that satisfy the equation. 3 sin(2x) = 3 cos(x)

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(1) Answers
jonathan1

3 sin ( 2 x ) = 3 cos x 3 · 2 sin x cos x - 3 cos x = 0 6 sin x cos x - 3 cos x = 0   /: 3 2 sin x cos x - cos x = 0 cos x ( 2 sin x - 1 ) cos x = 0,   x 1 = π/2,  x 2 = 3π/2; 2 sin x - 1 = 0 2 sin x = 1 sin x = 1/2 x 3 = π/6,  x 4 = 5π/6.

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