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How do I do this problem

How do I do this problem-example-1
User Stefanie
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1 Answer

6 votes

\sin(5\pi)/(12)

Notice that
(5\pi)/(12)=(3\pi)/(12)+(2\pi)/(12)=\frac\pi4+\frac\pi6. So,


\sin(5\pi)/(12)=\sin\left(\frac\pi4+\frac\pi6\right)

By the angle sum identity for sine, this is equal to


\sin\left(\frac\pi4+\frac\pi6\right)=\sin\frac\pi4\cos\frac\pi6+\cos\frac\pi4\sin\frac\pi6=\frac1{\sqrt2}*\frac{\sqrt3}2+\frac1{\sqrt2}*\frac12=(\sqrt3+1)/(2\sqrt2)
User Fmoo
by
8.1k points

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