Solve sin4/3pi

$$\sin \frac { 4 } { 3 } \pi$$

Evaluate

$$-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Solution Steps

Use \sin(x+y)=\sin(x)\cos(y)+\sin(y)\cos(x) where x=\pi and y=\frac{\pi }{3} to obtain the result.

$$\sin(\pi +\frac{\pi }{3})=\sin(\pi )\cos(\frac{\pi }{3})+\sin(\frac{\pi }{3})\cos(\pi )$$

Get the value of \sin(\pi ) from trigonometric values table.

$$0\cos(\frac{\pi }{3})+\sin(\frac{\pi }{3})\cos(\pi )$$

Get the value of \cos(\frac{\pi }{3}) from trigonometric values table.

$$0\times \frac{1}{2}+\sin(\frac{\pi }{3})\cos(\pi )$$

Get the value of \sin(\frac{\pi }{3}) from trigonometric values table.

$$0\times \frac{1}{2}+\frac{\sqrt{3}}{2}\cos(\pi )$$

Get the value of \cos(\pi ) from trigonometric values table.

$$0\times \frac{1}{2}+\frac{\sqrt{3}}{2}\left(-1\right)$$

Do the calculations.

$$-\frac{\sqrt{3}}{2}$$