Question

How to solve for sin(8pi/15)cos(pi/5)-cos(8pi/15)sin(pi/5) using values on the unit circle and not decimal values?

Answer 1

\[
\sin(A-B) = \sin(A)\cos(B)-\cos(A)\sin(B)
\]

Answer 2

\[
\sin(8\pi/15)\cos(\pi/5)-\cos(8\pi/15)\sin(\pi/5) = \sin(8\pi/15-\pi/5) = \\
\sin(8\pi/15-3\pi/15) = \sin((8\pi-3\pi)/15) = \sin(5\pi/15) =
\sin(\pi/3) = \sqrt{3}/2
\]