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Find the value of the expression below. I used the angle sum formula and it didn't work.

 Aug 9, 2022

Best Answer 

 #1
avatar+33151 
+3

The angle sum formula should work:

 

\(\sin {(\frac{2\pi}{15})}\cos {(\frac{4\pi}{5})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{4\pi}{5})}\\ =\sin {(\frac{2\pi}{15})}\cos {(\frac{12\pi}{15})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{12\pi}{15})}\\ =\sin {(\frac{-10\pi}{15})}\\ =\sin{\frac{-2\pi}{3}}\\ = -\frac{\sqrt 3}{2}\)

 Aug 9, 2022
 #1
avatar+33151 
+3
Best Answer

The angle sum formula should work:

 

\(\sin {(\frac{2\pi}{15})}\cos {(\frac{4\pi}{5})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{4\pi}{5})}\\ =\sin {(\frac{2\pi}{15})}\cos {(\frac{12\pi}{15})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{12\pi}{15})}\\ =\sin {(\frac{-10\pi}{15})}\\ =\sin{\frac{-2\pi}{3}}\\ = -\frac{\sqrt 3}{2}\)

Alan Aug 9, 2022

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