You can put this solution on YOUR website!
How do I find the exact value of sin(5pi/8)? I don't know how to start this one. Do I use a double angle or half angle formula?
What you want to do here is to come up with a denominator like 2, 3, 4, & 6 that divides into 180º evenly to a special angle like 30º, 45º, 60º, etc. The half-angle formula for sin will do it.
sin x/2=±√((1-cos x)/2) (note that we are doubling the angle in the radical)
For given problem:
cos(5π/4)=-√2/2 (note:5π/4 is in quadrant III where cos is negative)
sin (5π/8)=√((1+√2/2)/2)=√((2+√2)/4)=√(2+√2)/2 (note: 5π/8) is in quadrant II where
sin is positive, so we choose the positive root)