Find the function value

Question

Find the function value.

sin ^2 (7∏ / 8)

Answer 1

sin(θ/2) = ±√ [(1 - cosθ) / 2 ]

So, sin²(θ/2) = (1 - cosθ) / 2

sin²(7π/8) = sin²[ (7π/4) / 2 ] = (1 - cos(7π/4)) / 2 = (1 - √2/2) / 2 = (2 - √2) / 4