Question

How do you find the exact values of COS(-337.5) using the half angle formula?

Answer 1

Find cos (-337.5)
Answer: `+- sqrt(2 + sqrt2)/2`

Explanation:

Call cos (-337.5) = cos t --> cos (2t) = cos (675)
Apply the trig identity: cos 2t = 2cos^2 t - 1
On the trig unit circle,
`cos (2t) = cos (675) = cos (-45 + 2(360)) = cos 45 = sqrt2/2`

Therefor, `sqrt2/2 = 2cos^2 t - 1` --> `cos^2t = (2 + sqrt2)/4`->

`cos t = cos (-337.5) = +- sqrt(2 + sqrt2)/2`