00:01
We have to solve cosine 2 theta plus 2 cosine squared theta equals 2.
00:06
For all values of theta between 0 degrees and 360 degrees, we're going to start by substituting for this double angle.
00:16
So cosine of 2 theta is equal to cosine squared theta minus sine squared theta.
00:27
And then we're going to bring down plus two cosine squared theta and set that equal to two.
00:35
So we have some like terms to combine.
00:38
We can combine this cosine squared theta and this two cosine squared data to make three cosine squared theta.
00:47
Then we have minus sine square theta and we'll set that equal to two.
00:54
So we have some pythagorean identities we can use.
01:00
I'll use the pythagorean identity to substitute for cosine squared data.
01:06
So we'll bring down the three.
01:09
So cosine squared theta is equal to 1 minus sine square data.
01:15
And then we'll bring down the minus sine squared data and we'll set that equal to 2.
01:22
Now we'll distribute the three.
01:24
So we have 3 minus 3, sine squared theta, minus sine square theta, equals 2.
01:37
We can combine these like terms right here.
01:44
So when we do that, we get negative 4, sine square theta plus 3 equals 2.
01:55
Next, we can subtract three from both sides.
02:02
That leaves us with negative 4, sine squared theta equals negative 1.
02:09
We can divide both sides by negative 4, and we end up with the equation sine squared theta equals 1 fourth.
02:22
So we can solve this using square roots.
02:25
So you can take the square root of both sides.
02:28
That leaves me with sine square theta equals plus or minus.
02:34
Square root of one is one over square of four is two...