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

Question

Mathematics

Sean Weeks

22 June, 17:01

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

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Answers (1)

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Marianna Gardner · Answer 1

0, π, 7π/6, 11π/6, 2π.

Step-by-step explanation:

sin Ф + 1 = cos 2 Ф 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.