Question

Find the exact value of sin22.5 (using the half angle formula)

Answer 1

sin(a/2) = √(1/2(1 - cos a))
sin 22.5 = sin (45/2) = √(1/2(1 - cos 45)) = √(1/2(1 - 1/√2)) = √(1/2(√2 - 1)/√2) = √(√2/4(√2 - 1)) = √(2 - √2)/2