Question

How do you find the value of `cos (theta/2)` given `sintheta=-7/25` and `270<theta<360`?

Answer 1

`- (7sqrt2)/10`

Explanation:

`sin t = -7/25`. Find cos t.
`cos^2 t = 1 - sin^2 t = 1 - 49/625 = (625 - 49)/625 =`
`= 576/625`
`cos t = 24/25` (since t is in quadrant IV)
Use the identity:
`2cos^2 a = 1 + cos 2a`
`2cos^2 (t/2) = 1 + cos t = 1 + 24/25 = 49/25`
`cos^2 (t/2) = 49/50`
`cos (t/2) = - 7/(5sqrt2)` (because t/2 is in Quadrant II)
`cos (t/2) = - (7sqrt2)/10`