Question 667117
<pre>
Use an Addition or Subtraction Formula to find the exact value of the expression.
sin( -5&#960;/12)
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@Lynnlo's answer: 0.9659======OR===========-1+√3/2√2, is ALL WRONG!
Isn't the EXACT value needed? .9659 is certainly NOT THAT!! And, I have no idea what "-1+√3/2√2" is!!
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You can use either, sin (A - B) = sin A cos B - cos A sin B (DIFFERENCE-of-2 ANGLES formula), or 
                    sin (A + B) = sin A cos B + cos A sin B (SUM-of-2 ANGLES formula)

<font color = blue><font size = 4><b>Using sin (A - B) = sin A cos B - cos A sin B (DIFFERENCE-of-2 ANGLES formula)</font></font></b>

{{{highlight(sin (- 5pi/12))}}} = {{{sin (4pi/12 - 9pi/12)}}} = {{{highlight(sin (pi/3 - 3pi/4))}}}

  sin (A - B) = sin A cos B - cos A sin B
{{{sin (pi/3 - 3pi/4) = sin (pi/3) cos (3pi/4) - cos (pi/3) sin (3pi/4)}}}, with {{{matrix(2,1, A = pi/3, B = 3pi/4)}}} 
{{{highlight(sin (pi/3 - 3pi/4)) = (sqrt(3)/2)(- sqrt(2)/2) - (1/2)(sqrt(2)/2)}}} = {{{highlight(- sqrt(6)/4 - sqrt(2)/4)}}} = {{{highlight((- sqrt(6) - sqrt(2))/4)}}}
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<font color = blue><font size = 4><b>Using sin (A + B) = sin A cos B + cos A sin B (SUM-of-2 ANGLES formula)</font></font></b>

{{{highlight(sin (- 5pi/12))}}} = {{{sin (- 3pi/12 + (- 2pi)/12)}}} = {{{highlight(sin (- pi/4 + (- pi)/6))}}}

     sin (A + B) = sin A cos B + cos A sin B
{{{sin (- pi/4 + (- pi)/6) = sin (- pi/4) cos (- pi/6) + cos (- pi/4) sin (- pi/6)}}}, with {{{matrix(2,1, A = - pi/4, B = - pi/6)}}} 
{{{highlight(sin (- pi/4 + (- pi)/6)) = (- sqrt(2)/2)(sqrt(3)/2) + (sqrt(2)/2)(- 1/2)}}} = {{{highlight(- sqrt(6)/4 + (- sqrt(2))/4)}}} = {{{highlight((- sqrt(6) - sqrt(2))/4)}}}</pre>