Question

The value of sin(pi/3)cos(pi) is A) -√ 3/2 B) 1/2 C) -1/2 D) 0

Answer 1

Look at the picture.

$\sin\dfrac{\pi}{3}=\dfrac{\sqrt3}{2}\\\\\cos\pi=-1\\\\\sin\dfrac{\pi}{3}\cdot\cos\pi=\dfrac{\sqrt3}{2}\cdot(-1)=-\dfrac{\sqrt3}{2}$

$Answer:\ \boxed{A)\ -\dfrac{\sqrt3}{2}}$

Answer 2

take a good peek at  your Unit Circle, if you don't have one, this is a great time to get one, many you can find online, those two angles are pretty well known.

$\bf sin\left( \frac{\pi }{3} \right)cos(\pi )\implies \cfrac{\sqrt{3}}{2}\cdot -1\implies -\cfrac{\sqrt{3}}{2}$