Question

How do you solve `62 sin^2 θ − cos 2θ = 0`?

Answer 1

Solve `62 sin^2 x - cos 2x = 0`

Explanation:

Replace cos 2x by `(1 - 2sin^2 x)`

`62sin^2x - 1 + 2sin^2 x = 0`

`64sin^2 x = 1` --> `sin x = +- 1/8`

`sin x = 1/8`= 0.125 --> `x = 7.18` deg and `x = (180 - 7.18) = 172.82` deg

`sin x = -1/8 = - 0.125` --> `x = (180 + 7.18) = 187.18` and `x = (360 - 7.18) = 352.82` deg.
Within interval `(0, 2pi)`, there are 4 answers:
7.18 deg, 172.82 deg; 187.18 deg, and 352.82 deg.