Expert: Sherry Wallin - 12/7/2009

Question
how do u figure out what the general solutions for cos(theta)=
-3/5?

Answer
Meema~
    What you really want to know is what angle theta gives you the cosine of it to be -3.5 and all you have to do is take the arccos(cos(theta)) = arccos(-3/5) because the arccos(cos(theta)) = theta.
I get theta is 53.13 deg but you need to determine which quadrant the angle is in. Since the cosine can be thought of as the x variable and it is a negative number that means the angle is either in the 2nd or 3rd quadrant. So your 'reference' angle is 53.13 deg. So the general solution would be
theta = 180 -53.13 = 126.87 deg or 180 + 53.13 = 233.13 deg.

Math Prof