SOLUTION: Evaluate sin(cos^-1(1/2)+cos^-1(1/3)) (cos^-1 = cos inverse)

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Question 1200010: Evaluate sin(cos^-1(1/2)+cos^-1(1/3))
(cos^-1 = cos inverse)
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Evaluate sin(cos^-1(1/2)+cos^-1(1/3)).
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Let a = cos^-1(1/2),  b = cos^-1(1/3)  be the angles, in radians.


Then sin(a) = sqrt%281+-+%281%2F2%29%5E2%29 = sqrt%283%29%2F2,

     sin(b) = sqrt%281+-+%281%2F3%29%5E2%29 = %282%2Asqrt%282%29%29%2F3.


The problem asks then about sin(a+b).  It is


    sin(cos^-1(1/2)+cos^-1(1/3)) = sin(a)*cos(b) + cos(a)*sin(b) = %28sqrt%283%29%2F2%29%2A%281%2F3%29 + %281%2F2%29%2A%28%282%2Asqrt%282%29%29%2F3%29 = 

                                 = sqrt%283%29%2F6 + %282%2Asqrt%282%29%29%2F6 = %28sqrt%283%29%2B2%2Asqrt%282%29%29%2F6 = 0.76008  (rounded).    ANSWER

Solved.