Question

How do you use a half-angle identity to find cos x, for `x= ((5pi)/12)`?

Answer 1

Find cos x = cos (5pi)/12

Explanation:

On the trig unit circle,

`cos 2x = cos ((10pi)/12) = cos ((5pi)/6) = - cos (pi/6) = -(sqrt3)/2`

Use trig identity: `2cos^2 x = 1 + cos 2x`

`2cos^2 x = 1 - (sqrt3)/2 =` 0.134

`cos^2 x = 0.067` --> `cos x = 0.26`