Question 805071: cos(41pi/12)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website!
Evaluate
cos(41pi/12)
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(41pi/12)is like rotating,36π/12=3π, counter clockwise around a unit circle plus an additional 5π/12 which places the reference angle of 5π/12 in quadrant III where cos<0)
..
cos(41pi/12)=-cos(5π/12)
cos(5π/12)=cos(9π/12-4π/12)=cos(3π/4-π/3)
Identity: cos(x-y)=cosxcosy+sinxsiny
cos(3π/4-π/3)=cos(3π/4)*cos(π/3)+sin(3π/4)*sin(π/3)
=-√2/2*1/2+√2/2*√3/2)=-√2/4+√6/4=(-√2+√6)/4
Calculator Check:
cos(41π/12)≈-0.2588..
Exact value=-(-√2+√6)/4≈-0.2588..
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