Question

Use a half-angle identity to find the exact value of each expression.

sin 22.5°

Answer 1

Explanation:

sin(22.5°) = √(1 - cos 22.5°)/2

= √(1 - (√2/2)²)/2

= √(1 - (2 - 2√2)/4)/2

= √(1/4)/2

= √(1/16)

= 1/4