Solve cos x = sin 2x on [0, 2 pi]?

Question

Solve cos x = sin 2x on [0, 2 pi]?

Answer 1

sin(2x) is a double angle and is equal to sin(2x) = 2sin(x)cos(x)

so your equation becomes

cos x = sin 2x

cos x = 2sin(x)cos(x)

[ Now, divide both sides by cos(x)]

1 = 2sin(x)

[Now, divide by 2 on both sides]

(1/2) = sinx

[use SOH CA TOA to draw your traingle]

[http://www.battaly.com/calc/precalc/30_6...        30°= π/6]

x = π/6, 5π/6