How do you solve 2 cos 2θ = 4 - 5 cos θ?

1 Answer
Nghi N.
Jul 19, 2015

Solve 2cos 2x = 4 - 5cos x

x = +-41.41 deg

Explanation:

Use trig identity: cos 2x = 2cos^2 x - 1
2(2cos^2x - 1) + 5cos x - 4 = 0
4cos^2 x + 5cos x - 6 = 0. Call cos x = y, and solve
4y^2 + 5y - 6 = 0.
(4y - 3)(y + 2) = 0

y = 3/4 and y = 2 (rejected since > 1)

y = cos x = 3/4 --> x = +- 41.41 deg

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
2378 views around the world
You can reuse this answer
Creative Commons License