Find all exact solutions on the interval [0, 2π). (Enter your answers as a comma-separated list.) cos(2t) = −sin(t)

Answer 1

cos^2 - sin^2 = -sin

(1 - sin^2) - sin^2 = -sin

1 - 2sin^2 = -sin

2 sin^2 - sin - 1 = 0

2 M^2 - M - 1 = 0 where M = sin

( 2M + 1 )( M - 1 ) = 0

M = -1 or M = -1/2

sin t = -1 or sin t = -1/2

t = 270 or t = 210 or 330

t = 7 pi 6, 3 pi /2, 11 pi / 6