## anonymous one year ago Could somebody explain how to use the half-angle identity to find the exact value of sin(5pi/12)?

1. P0sitr0n

So basically you can use the fact that $\sin(2\alpha)=2\sin(\alpha)\cos(\alpha)$ Then, $\sin(\frac{5 \pi}{12})\ = 2 \sin (\frac{5 \pi} {6})\cos(\frac{5 \pi}{6})$ But you know the values of both functions at the point $\alpha = \frac{5 \pi}{6}$ (0.5 and $\frac{-\sqrt{3}}{2}$) respectively

2. anonymous

Thank you!