Answer:
±[tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex]
Step-by-step explanation:
We can rewrite [tex]sin(\frac{7\pi }{12} )[/tex] as [tex]sin(\frac{7\pi }{6} (\frac{1}{2} ))[/tex]. The half-angle identity for sin tells us that [tex]sin(\frac{x}{2} ) = \sqrt{\frac{1 - cos(x)}{2} }[/tex] (plus or minus). Now, we can plug in [tex]\frac{7\pi }{6}[/tex] for x. When we do that, we get [tex]\sqrt{\frac{1 - (-\frac{\sqrt{3}}{2}) }{2} }[/tex] = ± [tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex].
Hope this helped! :)
