Question

How do you use the half angle identify to find the exact value of `sin(pi/8)`?

Answer 1

`sin (pi/8) = sqrt(2 - sqrt2)/2`

Explanation:

Use trig identity:
`2sin^2 a = 1 - cos 2a`
In this case,
`a = pi/8` and `2a = pi/4` --> `cos pi/4 = sqrt2/2` -->
`2sin^2 (pi/8) = 1 - sqrt2/2 = (2 - sqrt2)/2`
`sin (pi/8) = +- sqrt(2 - sqrt2)/2`
Since (pi/8) is in Q. 1, take the positive value.
`sin (pi/8) = sqrt(2 - sqrt2)/2`