Question

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

Answer 1

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

Answer 2

Thank you!