00:01
For this problem, we want to find the value of cosine of theta minus v.
00:04
Given the value of cosine of theta, which is equal to 3 over 5, with theta in the fourth quadrant, and tangent fee equal to negative square to 15, where fee is in quadrant 2.
00:16
Now we recall cosine of theta minus fee is equal to cosine of theta times cosine of fee plus sine of theta times sine of f.
00:27
In this identity, we only have to, have a value for cosine theta.
00:32
So we still have to find cosine fee, sine theta, and a sign of fee.
00:38
Now for sign of theta, we will use the information of cosine theta, which is equal to 3 over 5, where theta is in quadrant 4.
00:51
If we are to draw this one, it should look like this.
00:55
This being the terminal side, and then this will be our reference angle theta.
01:00
And since cosine theta is x over r, the radius will be 5 and the x value will be positive 3.
01:08
So we still have to find y, and to do that, we will use pythagorean theorem.
01:15
So in pythagorean theorem, that's 3 squared plus y squared equal to 5 squared, which means y squared is equal to 16...