How do you use the half angle formula to find sin ((9pi)/ 8)?

1 Answer
Mar 12, 2018

sin((9pi)/8) = -sqrt(2-sqrt2)/2

Explanation:

First reduce the angle to the first quadrant:

sin((9pi)/8) = sin(pi+pi/8)

sin((9pi)/8) = sin(pi)cos(pi/8)+cos(pi)sin(pi/8) = -sin(pi/8)

Now use:

sin(pi/8) = sqrt((1-cos(pi/4))/2)

sin(pi/8) = sqrt((1-sqrt2/2)/2)

sin(pi/8) = sqrt((2-sqrt2)/4)

sin(pi/8) = sqrt(2-sqrt2)/2

and finally:

sin((9pi)/8) = -sqrt(2-sqrt2)/2