Question 808517
Use double or half angle formula to determine the value of the trigonometric function sin(19pi/12) 
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use sin half-angle formula: {{{sin(s/2)=sqrt((1-cos(s))/2)}}}
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sin(19pi/12)=sin(38π/12)/2=sin(19π/6)/2=sin(3π+π/6)/2
reference angle for (3&#960;+&#960;/6)=7&#960;/6 in quadrant III where sin<0, cos<0
sin(19&#960;/12)=sin(3&#960;+&#960;/6)/2=sin(7&#960;/6)/2=
{{{(sin(7pi/6)/2)=-sqrt((1-cos(7pi/6))/2)=-sqrt((1-(- sqrt(3)/2)/2))=-sqrt((2+sqrt(3))/4))}}}
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calculator check:(Use sin key set to radians)
sin(19&#960;/12)&#8776;-0.9659..
Exact answer as calculated={{{-sqrt((2+sqrt(3))/4))}}}&#8776;-0.9659..