Question

Given `costheta=4/5` and `270<theta<360`, how do you find `cos (theta/2)`?

Answer 1

`- (3sqrt10)/10`

Explanation:

Use trig identity:
`1 + cos 2a = 2cos^2 a`
`2cos^2 (t/2) = 1 + cos t = 1 + 4/5 = 9/5`
`cos^2 (t/2) = 9/10`
`cos (t/2) = +- 3/sqrt10 = (3sqrt10)/10`.
Since t is in Quadrant IV, then, t/2 is in Quadrant II.
cos (t/2) is negative.
`cos (t/2) = - (3sqrt10)/10`