00:01
We are going to write this equation in terms of a single angle.
00:08
So it's 2 -sign 2 -theta minus 3 -sign theta.
00:15
And we want all the values between 0 and 2 -pi.
00:24
So that is a full circle.
00:28
Okay, so this first one, i can use my double -angle formulas to change it to 2 times 2 -sign theta, cosine theta.
00:42
Minus 3, sine theta.
00:47
Distribute this two, that leads me with 4, sine theta, minus 3, sine theta.
00:57
Now, both of these values have a sine theta that i can factor out.
01:01
So i'm going to factor out a sine theta at this first one, which leaves me sine theta times 4 minus cosine theta, minus 3.
01:12
So all of these, it equals 0.
01:14
So we have two different parts of this equation.
01:17
We want to figure out when sine of theta equals zero.
01:23
So looking at our unit circle here, this is zero, this is pi over two, this is pi, and this is three pi over two, and this is also two pi when we go back around again.
01:36
So values where sign equals zero is when it doesn't have any up or down values.
01:43
So it's not going vertical.
01:50
So the only time when sign is zero is when i have my horizontal lines here at zero and at pi.
01:56
So those are two answers, zero and pi.
01:59
Now we need to figure out what values make this inside part equal zero...