Question

How do you use a half-angle formula to simplify `cos(-337.5)`?

Answer 1

Use the trig identity: 2cos^2 x = 1 - cos 2x

`2cos(-337.5)^2 = 1 - cos (675)`

On the trig unit circle,
`cos (675) = cos (-45 + 2(360)) = cos 45 = sqrt2/2`

`cos^2 (-375) = 1 - (sqrt2)/2 = (2 - sqrt2)/4`