Question

Using half angle identities, find an EXACT expression for sin(7π/12).

Answer 1

Answer:

±$\frac{1+\sqrt{3} }{2\sqrt{2} }$

Step-by-step explanation:

We can rewrite $sin(\frac{7\pi }{12} )$ as $sin(\frac{7\pi }{6} (\frac{1}{2} ))$. The half-angle identity for sin tells us that $sin(\frac{x}{2} ) = \sqrt{\frac{1 - cos(x)}{2} }$ (plus or minus). Now, we can plug in $\frac{7\pi }{6}$ for x. When we do that, we get $\sqrt{\frac{1 - (-\frac{\sqrt{3}}{2}) }{2} }$ =  ± $\frac{1+\sqrt{3} }{2\sqrt{2} }$.

Hope this helped! :)