Question 864341
Help with this problem? I need help on how to work out this problem. Thank you! 
Use a double- or half-angle formula to determine the value of the trigonometric function. 
sin(27pi/8)
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Use half-angle formula for sin: {{{sin(x/2)=(sqrt(1-cosx)/2)}}}
{{{sin(27pi/8)=(27pi/4)/2}}}
{{{27pi/4=24pi/4+3pi/4=6pi+3pi/4}}}=reference.angle of (3pi/4) in quadrant II
{{{cosx=cos(3pi/4)=-sqrt(2)/2}}}
{{{sin(27pi/8)=(27pi/4)/2=-sqrt((1+sqrt(2)/2)/2)=-sqrt(2+sqrt(2))/2)}}}
calculator check:
sin(27π/8)≈0-0.9238
exact value={{{-sqrt(2+sqrt(2))/2)}}}≈-0.9238