Answer:
[tex]\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]
Step-by-step explanation:
We know that coordinate of any point on unit circle is given by
[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]
Given that [tex]\theta=-\frac{4\pi}{3}[/tex]
So we just need to plug the value of given angle [tex]\theta=-\frac{4\pi}{3}[/tex] into above formula:
[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]
[tex]=\left(\cos\left(-\frac{4\pi}{3}\right),\sin\left(-\frac{4\pi}{3}\right)\right)[/tex]
[tex]=\left(\cos\left(2\pi-\frac{4\pi}{3}\right),\sin\left(2\pi-\frac{4\pi}{3}\right)\right)[/tex]
[tex]=\left(\cos\left(\frac{2\pi}{3}\right),\sin\left(\frac{2\pi}{3}\right)\right)[/tex]
[tex]=\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]
Hence choice (3) is correct.
