Question

How do you solve `4sinx-3sin2x=0` for `0<=x<=360`?

Answer 1

`0, 48^@19, 180^@, 311^@81, 360^@`

Explanation:

Since sin 2x = 2sin x.cos x, we get:
4sin x - 6sin x.cos x = 0
sin x(4 - 6cos x) = 0
Trig table and unit circle -->
a. sin x = 0 --> `x = 0`, `x = 180^@`, and `x = 360^@`
b. 4 - 6cos x = 0
cos x = 4/6 = 2/3 --> x = +- 48^@19
Arc (-48.19) and arc (360 - 48.19 = 311.81) are co-terminal
Answers for (0, 360)
`0, 48^@19, 180^@, 311^@81, 360^@`