00:01
All right, in this problem, we're trying to solve sign of 2 theta plus sine of theta equal to 0 on the interval 0 to 2 pi, not including 2 pi.
00:10
So first thing i want to do is i'm going to use my identity here, that sine of 2 theta is equal to sine theta times cosine.
00:16
2 times sine theta, 2 times cosine theta.
00:19
So i'm going to swap that out for the sine of 2 theta.
00:22
So 2 times the sine of theta plus the sine of theta is equal to 0.
00:29
Since these both have a sine theta in common, i could factor that out to the front.
00:33
So that's two times the cosine theta plus one and that equals zero.
00:38
And i apply zero product property and say sign theta is equal zero and two times the cosine of theta plus one equals 0.
00:46
I subtract one of both sides.
00:48
So two cosine theta equals negative one...