Question

How do you find the exact values of sin 75 degrees using the half angle formula?

Answer 1

Find: sin 75 deg
Answer: `sin 75 = +- sqrt(2 + sqrt3)/2`

Explanation:

Call sin 75 = sin t --> cos 150 = cos 2t
On the trig unit circle,
cos (150) = cos (180 - 30) = - cos 30 =`-(sqrt3)/2`
`cos 150 = (-sqrt3)/2 = 1 - 2sin^2 t`
`2sin^2 t = (2 + sqrt3)/2`

`sin (75) = sin t = +- (sqrt(2 + sqrt3))/2`