# SOLUTION: 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? Thank you!!

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 Click here to see ALL problems on Trigonometry-basics Question 479877: 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? Thank you!!Answer by lwsshak3(6505)   (Show Source): 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: sin (5π/8)/2=±√(1-cos(5π/4)/2) 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) ans: sin (5π/8)=√(2+√2)/2