Question

Use a double or half angle formula to determine value of cos(13π/12)?

Answer 1

`- (2 + sqrt3)/2`

Explanation:

`cos ((13pi)/12) = cos (pi/12 + pi) = - cos (pi/12)`
Find `cos ((pi)/12)` by using trig identity:
`2cos^2 a = 1 + cos 2a`.
In this case:
`2cos^2 (pi/12) = 1 + cos (pi/6) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = (2 + sqrt3)/2` --> (`cos (pi/12)` is positive).
Finally,
`cos ((13pi)/12) = - cos (pi/12) = - (2 + sqrt3)/2`