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the reference angle of 9pi/8 is 22.5 degrees which is HALF of 45 degrees

So, we can use the Half Angle formula:

cos(1/2(45)) = +/- sqrt[(1+cos45)/2)] = +/- sqrt[(1+ sqrt(2)/2)/2)]

= - sqrt[(2+sqrt(2)/4] it's negative because the angle lies in the 3rd quadrant.

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