the problem is Given cos2x = 7/32, tan2x<0 and -\pi/2<x<\pi/2, find sin x
because
-\pi/2<x<\pi/2 means the answer would be either in the first or forth quadrant and tan2x has to be smaller than 0 so if the cos is positive, then the sin has to be negative?
Is this why there is only -5/8 as the answer instead of + or - 5/8 because of the square root when I took out the ?
Wait, but we are only given cos2x = 7/32
so there's no cos. but -\pi/2<x<\pi/2 so that means x has to be in the first or forth quadrant of the unit circle and cosine is always positive in those qudrants. So would that mean I have a pos cos, and negative sin?
I'm not sure how to solve for just the cos of x and then plug it into the tan2x formula...