Question 805071

Evaluate
cos(41pi/12)
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(41pi/12)is like rotating,36&#960;/12=3&#960;, counter clockwise around a unit circle plus an additional 5&#960;/12 which places the reference angle of 5&#960;/12 in quadrant III where cos<0)
..
cos(41pi/12)=-cos(5&#960;/12)
cos(5&#960;/12)=cos(9&#960;/12-4&#960;/12)=cos(3&#960;/4-&#960;/3)
Identity: cos(x-y)=cosxcosy+sinxsiny
cos(3&#960;/4-&#960;/3)=cos(3&#960;/4)*cos(&#960;/3)+sin(3&#960;/4)*sin(&#960;/3)
=-&#8730;2/2*1/2+&#8730;2/2*&#8730;3/2)=-&#8730;2/4+&#8730;6/4=(-&#8730;2+&#8730;6)/4
Calculator Check:
cos(41&#960;/12)&#8776;-0.2588..
Exact value=-(-&#8730;2+&#8730;6)/4&#8776;-0.2588..