Find the exact value of: sin13pi/8

Sin (13π/8), is in quadrant IV so the angle will be negative, find the reference angle.

sin (13π/8) = - sin (16π/8 - 13π/8) = - sin (3π/8) = - cos (4π/8 - 3π/8) = - cos (π/8).

Use half angle formula for cos (x):

cos² (x/2) = (cos (x) + 1) / 2

Let x = π/4

cos² (π/8) = (cos (π/4) + 1) / 2

cos² (π/8) = (√ (2) / 2 + 1) / 2

cos (π/8) = √ (√ (2) / 4 + 1/2)

-cos (π/8) = - √ ((√ (2) + 2) / 4)