Question

How do you find the value of `sin (22 1/2)` using the double or half angle formula?

Answer 1

`sin (22.5) = sqrt(2 - sqrt2)/2`

Explanation:

Use trig identity:
`2sin^2 a = 1 - cos 2a`
In this case, `a = (22^@5)` and `2a = 45^@` -->
`2sin^2 (22.5) = 1 - cos 45 = 1 - sqrt2/2 = (2 - sqrt2)/2`
`sin^2 (22.5) = (2 - sqrt2)/4`
`sin (22.5) = +- sqrt(2 - sqrt2)/2`
Since sin (22.5) is positive, take the positive value.
`sin (22.5) = sqrt(2 - sqrt2)/2`