How do you evaluate $sin (\frac{π}{12}) \cdot cos (3 \frac{π}{4}) - cos (\frac{π}{12}) \cdot sin (3 \frac{π}{4})$ $sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)$ ?

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How do you evaluate $sin (\frac{π}{12}) \cdot cos (3 \frac{π}{4}) - cos (\frac{π}{12}) \cdot sin (3 \frac{π}{4})$ $sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)$ ?

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Answer 1 · 2018-06-27T02:57:45

$- \frac{\sqrt{3}}{2}$ $-sqrt3/2$

Explanation:

Recall

$sin (A - B) = sin A cos B - cos A sin B$ $sin(A-B)=sinAcosB-cosAsinB$

$sin (\frac{π}{12}) cos (\frac{3 π}{4}) - cos (\frac{π}{12}) sin (\frac{3 π}{4}) = sin (\frac{π}{12} - \frac{3 π}{4})$ $sin(pi/12)cos((3pi)/4)-cos(pi/12)sin((3pi)/4)=sin(pi/12-(3pi)/4)$

$sin (\frac{π}{12} - \frac{9 π}{12})$ $sin(pi/12-(9pi)/12)$

Recall

$sin (- x) = - sin (x)$ $sin(-x)=-sin(x)$

$sin (- \frac{2 π}{3}) = - sin (\frac{2 π}{3})$ $sin(-(2pi)/3)=-sin((2pi)/3)$

$- \frac{\sqrt{3}}{2}$ $-sqrt3/2$

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How do you evaluate $sin (\frac{π}{12}) \cdot cos (3 \frac{π}{4}) - cos (\frac{π}{12}) \cdot sin (3 \frac{π}{4})$ $sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)$ ?

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How do you evaluate sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)sin(π12)⋅cos(3π4)−cos(π12)⋅sin(3π4)sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)?

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Explanation:

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How do you evaluate $sin (\frac{π}{12}) \cdot cos (3 \frac{π}{4}) - cos (\frac{π}{12}) \cdot sin (3 \frac{π}{4})$ $sin (pi / 12) * cos (3 pi / 4) - cos (pi / 12) * sin (3 pi / 4)$ ?