Question

How do you evaluate `cos ((13pi)/12)`?

Answer 1

`- sqrt(2 + sqrt3)/2`

Explanation:

`cos ((13pi)/12) = cos (pi/12 + pi) = - cos (pi/12)`
Evaluate cos (pi/12) by the trig identity:
`cos 2a = 2cos^2 a - 1`
`cos ((2pi)/12) = cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1`
`2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = sqrt(2 + sqrt3)/2` ( since `cos (pi/12`) is positive)
There for:
`cos ((13pi)/12) = -cos (pi/12) = - sqrt(2 + sqrt3)/2`