What is the exact value of sin (22.5 degrees)?

To find the exact value of sin(22.5°), we can use the half-angle formula. The half-angle formula for sine is:

sin(θ/2) = ± sqrt((1 - cos(θ))/2)

We know that 22.5° is half of 45°, so we can use cos(45°) in our formula. The cosine of 45 degrees is sqrt(2)/2 or 1/sqrt(2).

So,

sin(22.5°) = sqrt((1 - cos(45°))/2) = sqrt((1 - sqrt(2)/2)/2) = sqrt((2 - sqrt(2))/4) = sqrt(2 - sqrt(2))/2

So, the exact value of sin(22.5°) is sqrt(2 - sqrt(2))/2.