Question

Which point on the unit circle corresponds to −4π/3 ?

(1/2, −3√/2)
(-3√/2, 1/2)
(-1/2, 3√/2)
(3√/2, −1/2)

Answer 1

-1/2, √3/2

Explanation:

Answer 2

`\left(-(1)/(2),(√(3))/(2)\right)`

Explanation:

We know that coordinate of any point on unit circle is given by

`\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)`

Given that
`\theta=-(4\pi)/(3)`

So we just need to plug the value of given angle
`\theta=-(4\pi)/(3)` into above formula:

`\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)`

`=\left(\cos\left(-(4\pi)/(3)\right),\sin\left(-(4\pi)/(3)\right)\right)`

`=\left(\cos\left(2\pi-(4\pi)/(3)\right),\sin\left(2\pi-(4\pi)/(3)\right)\right)`

`=\left(\cos\left((2\pi)/(3)\right),\sin\left((2\pi)/(3)\right)\right)`

`=\left(-(1)/(2),(√(3))/(2)\right)`

Hence choice (3) is correct.