How do you evaluate $sin (\frac{π}{12})$ $sin ((pi)/12)$ ?

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How do you evaluate $sin (\frac{π}{12})$ $sin ((pi)/12)$ ?

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Answer 1 · 2016-04-23T09:29:50

Using formula $sin θ = \sqrt{\frac{1}{2} \times (1 - cos (2 θ))}$ $sintheta=sqrt(1/2xx(1-cos(2theta)))$
$sin (\frac{π}{12}) = \sqrt{\frac{1}{2} \times (1 - cos (2 \times \frac{π}{12}))}$ $sin(pi/12)=sqrt(1/2xx(1-cos(2xxpi/12))$
$= \sqrt{\frac{1}{2} \times (1 - cos (\frac{π}{6}))}$ $=sqrt(1/2xx(1-cos(pi/6))$
$= \sqrt{\frac{1}{2} \times (1 - \frac{\sqrt{3}}{2})}$ $=sqrt(1/2xx(1-sqrt3/2)$
$= \sqrt{\frac{1}{8} \times (4 - 2 \sqrt{3})}$ $=sqrt(1/8xx(4-2sqrt3)$
$= \sqrt{\frac{1}{8} \times ({(\sqrt{3})}^{2} + 1^{2} - 2 \sqrt{3} \cdot 1)}$ $=sqrt(1/8xx((sqrt3)^2+1^2-2sqrt3*1)$
$= \sqrt{\frac{1}{8} \times {(\sqrt{3} - 1)}^{2}}$ $=sqrt(1/8xx(sqrt3-1)^2)$
$= \frac{1}{2} \times \frac{1}{\sqrt{2}} \times (\sqrt{3} - 1) = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$ $=1/2xx1/sqrt2xx(sqrt3-1)=(sqrt3-1)/(2sqrt2)$

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How do you evaluate $sin (\frac{π}{12})$ $sin ((pi)/12)$ ?

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