Question

How do you use the half angle identity to find exact value of cos^2(pi/3)?

Answer 1

`cos^2(pi/3) = 1/4`

Explanation:

Let `u = (2pi)/3`, then `u/2 = pi/3`

We know that `cos^2(u/2) = (1+cos(u))/2`

By taking a peek at the unit circle we know that `cos(u) = -1/2`, so it's just a question of switching values.

`cos^2(u/2) = (1-1/2)/2 = (1/2)/2 = 1/2*1/2 = 1/4`

That being said, `pi/3` is a special angle (being 60º exactly) so it was easier to just evaluate it without using the formula.