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

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Answer 1 · 2018-03-12T15:22:20

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

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#