Question

What is the sine value of 2 pi over 3? negative 1 over 2 1 over 2 negative square root 3 over 2 square root 3 over 2

Answer 1

Answer:

$\large\boxed{\sin\dfrac{2\pi}{3}=\dfrac{\sqrt3}{2}}$

Step-by-step explanation:

$\sin\dfrac{2\pi}{3}=\sin\bigg(\pi-\dfrac{\pi}{3}\bigg)\\\\\text{use}\ \sin(x-y)=\sin x\cos y-\sin y\cos x\\\\=\sin\pi\cos\dfrac{\pi}{3}-\sin\dfrac{\pi}{3}\cos\pi\\\\\text{use the table from the attachment}\\\\\sin\pi=0\\\\\cos\dfrac{\pi}{3}=\dfrac{1}{2}\\\\\sin\dfrac{\pi}{3}=\dfrac{\sqrt3}{2}\\\\\cod\pi=-1\\\\\text{subtitute:}\\\\=(0)\left(\dfrac{1}{2}\right)-\left(\dfrac{\sqrt3}{2}\right)(-1)=\dfrac{\sqrt3}{2}$