Question 1200010
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Evaluate sin(cos^-1(1/2)+cos^-1(1/3)).
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<pre>
Let a = cos^-1(1/2),  b = cos^-1(1/3)  be the angles, in radians.


Then sin(a) = {{{sqrt(1 - (1/2)^2)}}} = {{{sqrt(3)/2}}},

     sin(b) = {{{sqrt(1 - (1/3)^2)}}} = {{{(2*sqrt(2))/3}}}.


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) = {{{(sqrt(3)/2)*(1/3)}}} + {{{(1/2)*((2*sqrt(2))/3)}}} = 

                                 = {{{sqrt(3)/6}}} + {{{(2*sqrt(2))/6}}} = {{{(sqrt(3)+2*sqrt(2))/6}}} = 0.76008  (rounded).    <U>ANSWER</U>
</pre>

Solved.