How do you find the exact value of $sin (\frac{7 π}{12})$ $sin ((7pi)/12)$ ?

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How do you find the exact value of $sin (\frac{7 π}{12})$ $sin ((7pi)/12)$ ?

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Answer 1 · 2016-04-09T07:49:22

$sin (7 \frac{π}{12}) = sin (\frac{π}{3} + \frac{π}{4})$ $sin(7pi/12)=sin(pi/3+pi/4)$
$= sin (\frac{π}{3}) cos (\frac{π}{4}) + cos (\frac{π}{3}) sin (\frac{π}{4})$ $=sin(pi/3)cos( pi/4)+cos(pi/3)sin(pi/4)$
$= \frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}} + \frac{1}{2} \times \frac{1}{\sqrt{2}} = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ $=sqrt3/2xx1/sqrt2+1/2xx1/sqrt2=(sqrt3+1)/(2sqrt2)$

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How do you find the exact value of $sin (\frac{7 π}{12})$ $sin ((7pi)/12)$ ?

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How do you find the exact value of $sin (\frac{7 π}{12})$ $sin ((7pi)/12)$ ?