Question

How do you find the general solutions for `sin 2 theta = cos theta`?

Answer 1

`pi/6; pi/2; (5pi)/6; (3pi)/2` + `(2kpi)`

Explanation:

sin 2t - cos t = 0
2sint.cos t - cos t = 0
cos t(2sin t - 1) = 0
Either factor should be zero.
a. cos t = 0
Unit circle give 2 solutions
`t = pi/2`, and `t = (3pi)/2`
b. 2sin t - 1 = 0 --> `sin t = 1/2`
Trig table and unit circle give:
`t = pi/6`, and `t = (5pi)/6`
Fro general answer, add `2kpi`