Question

How do I do this problem

Answer 1

`\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)`