00:01
So in this problem, we're being asked to solve the given equation, the sine of 2x plus the sign of x equal to 0 for all angles between 0 and 360 degrees.
00:09
Well, first off, we have the sign of 2x.
00:12
Well, remember, our double angle formula for sign says the sine of 2x is equal to 2 times the sine of x times the cosine of x.
00:19
So that's the first thing i'm going to do.
00:21
We're going to substitute that in, so that way all of our angles are in terms of x.
00:25
Next, because both terms contains this factor of sine of x, i'm going to factor that up.
00:29
So we'll have the sine of x, and what will remain is two times the cosine of x plus one.
00:36
So now that we've factored, we can set both our factors equal to zero.
00:40
So i'll have the sign of x equal to zero, or we can have two times the cosine of x plus one equal to zero.
00:46
So now for this first one, we have the sign of x equal to zero.
00:51
Well, remember, when sine is zero, that's going to be your y coordinates from your ordered pairs.
00:59
So if you're thinking about your coordinate plane, when is sine zero? well, that would happen at zero as well as 180 degrees.
01:07
So x could be zero or x could be 180...