Find cos(s + t) given that cos s = (1/3), with s in quadrant I, and sin t = - (1/2), with t in quadrant IV.

Answer 1

cos(s+t) = cos s cos t - sin s sin t

If cos s = 1/3 in the first quadrant, sin is positive, and sin = √1 - (1/3)² = √8/9 or 2√2 / 3

In the fourth quadrant, cos is positive, so if sin = -(1/2)), cos = √1 - (1/2)² = √3/4 = √3 / 2

Then, cos(s+t) = 1/3 * √3 / 2 - 2√2 / 3 * -1/2 = √3 / 6 + √2 / 3 = .7601