SOLUTION: if sin x = -12/13 with pie < x < 3pi/2 then sin (pie/3 + x) = ?

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Question 920830: if sin x = -12/13 with pie < x < 3pi/2 then sin (pie/3 + x) = ?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if sin t = -12/13 with pie < t < 3pi/2 then sin (pie/3 + t) = ?
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x and y are negative in QIII
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By definition, sin = y/r
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Since sin = -12/13, y = -12 and r = 13
Then x = -sqrt[13^2 - 12^2] = -5
So cos(t) = -5/13
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Your Problem::
sin(pi/3 + t) = sin(pi/3)cos(t) + cos(pi/3)sin(t)
= sqrt(3)/2*(-5/13) + (1/2)*-12/13
etc.
Cheers,
Stan H.
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