Question

Solve sin Ф + 1 = cos 2Ф on the interval 0 ≤ Ф <2pi

Answer 1

0, π, 7π/6, 11π/6, 2π.

Explanation:

sin Ф + 1 = cos 2Ф using the identity cos2x = 1 - 2sin^2 x:

sin Ф + 1 = 1 - 2sin^2 Ф

2sin^2 Ф + sin Ф + 1 - 1 = 0

2sin^2 Ф + sin Ф = 0

sin Ф(2 sin Ф + 1 = 0

sin Ф = 0, sin Ф= -1/2

This gives Ф = 0, π, 2π, 7π/6, 11π/6.