Question

How do you find the exact values of sin^2(pi/6) using the half angle formula?

Answer 1

`sin^2(pi/6) = 1/4`

Explanation:

By the half angle formula
`color(white)("XXXX")` `sin^2(theta/2) = 1/2(1-cos(theta))`

For `theta = pi/3`
we have
`color(white)("XXXX")` `sin^2(pi/6) = 1/2( 1 - cos(pi/3))`

`color(white)("XXXX")` `color(white)("XXXX")` `=1/2(1 - 1/2)`

`color(white)("XXXX")` `color(white)("XXXX")` `= 1/4`

(of course, this assumes that you remembered `cos(pi/3) = 1/2` but didn't remember `sin(pi/6) = 1/2`).