+0

# Trig

0
135
1
+370

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

Aug 9, 2022

#1
+33343
+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
+33343
+3
$$\sin {(\frac{2\pi}{15})}\cos {(\frac{4\pi}{5})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{4\pi}{5})}\\ =\sin {(\frac{2\pi}{15})}\cos {(\frac{12\pi}{15})}-\cos {(\frac{2\pi}{15})}\sin {(\frac{12\pi}{15})}\\ =\sin {(\frac{-10\pi}{15})}\\ =\sin{\frac{-2\pi}{3}}\\ = -\frac{\sqrt 3}{2}$$