SOLUTION: how do I found the exact answer of sec(-5 pi/8)? I tried to add or subtract 2pi so that it is a value on the chart but that does not work and I don't know what else to try. I think

Question 689725: how do I found the exact answer of sec(-5 pi/8)? I tried to add or subtract 2pi so that it is a value on the chart but that does not work and I don't know what else to try. I think maybe a double angle therom or something?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
how do I found the exact answer of sec(-5 pi/8)?
use identity for cos half-angle formula: cos (s/2)=�√[(1+cos s)/2]
-sec(-5π/8)=-1/cos(-5π/8)
solve for cos(-5π/8), then take the negative reciprocal.
cos(-5π/8)=cos(-5π/4)/2)=-√[1+cos(-5π/4)/2]
cos(-5π/4)=cos π/4=-√2/2 in quadrant II where cos<0
-√[1+cos(-5π/4)/2]=-√[1-√2/2/2]=-√(2-√2)/2
-sec(-5π/8)=-1/cos(-5π/8)
-sec(-5π/8)=-1/-√(2-√2)/2
-sec(-5π/8)=2/√(2-√2)
check with computer:
cos(-5π/8)=-.3836
-sec(-5π/8)≈-1/-.3836=2.6131..
2/√(2-√2)≈2.6131..

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