00:01
For this question, we are going to use right triangle trig to help us find sign, cosine, and tangent of a double angle.
00:10
We are told that the angle is in quadrant three and that the cosine is negative two thirds.
00:25
Using pythagorean theorem, 3 squared, which is 9, minus a negative 2 squared, which is 4, gives us 5.
00:35
Take the square root, and we will label the other side.
00:38
With a negative root 5.
00:41
The negative is because of the location in quadrant 3.
00:46
Now i can find sine of 2x.
00:51
It is 2.
00:53
Sine x, cosine x.
00:58
Sign of x is opposite over hypotenuse.
01:05
Cosine of x is adjacent over hypotenuse.
01:12
Negative times negative is positive, 2 times 2 is 4 root 5 over 9.
01:23
Cosine of the double angle.
01:29
I have a choice of identities.
01:32
I will use cosine squared minus sine squared...