Question

Find the exact value of: sin13pi/8

Answer 1

Answer:

APEX answer:

-$-\frac{\sqrt{2+\sqrt{2} } }{\sqrt{4} }$

Step-by-step explanation:

Answer 2

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)