Question

How do you use half angle formula evaluate `sin(-67.5)` and `cos (pi/2)`?

Answer 1

Find `sin (-67.5) and cos (pi/2)`

Explanation:

Call sin (-67.5) = sin t --> cos 2t = cos (-135) = cos 135 = `-sqrt2/2`
Apply the trig identity: `cos 2t = 1 - 2sin^2 t`

`2sin^2 t = 1 + sqrt2/2 = (2 + sqrt2)/2`
`sin^2 t = (2 + sqrt2)/4`
`sin t = sin (-67.5) = +- sqrt(2 + sqrt2)/2`

Call `cos (pi/2) = cos y` --> `cos 2y = cos pi = - 1`
Apply trig identity: `cos 2y = 2cos^2 y - 1`
`- 1 = 2cos^2 y - 1`-> `2cos^2 y = 0` -->
`cos y = cos (pi/2) = 0`