Question

What is the answer to cos (3pi/8)?

Answer 1

`- (sqrt(2 - sqrt2)/2)`

Explanation:

Call `cos ((3pi)/8) = cos t` --> `cos 2t = cos ((3pi)/4) = -sqrt2/2`
Apply the identity;
`cos 2t = 2cos^2 t - 1 = - sqrt2/2`
`2cos^2 t = 1 - sqrt2/2 = (2 - sqrt2)/2`
`cos^2 t = (2 - sqrt2)/4`
`cos t = - (sqrt(2 - sqrt2))/2` --> since cos ((3pi)/4) is negative
Answer: `cos t = cos ((3pi)/4) = - (sqrt(2 - sqrt2))/2`