# How do you find the point (x,y) on the unit circle that corresponds to the real number t=(4pi)/3?

May 12, 2017

Point $\left(x , y\right)$ on unit circle corresponding to $\frac{4 \pi}{3}$ is $\left(- \frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$

#### Explanation:

Just remember that coordinates on the unit circle can be derived using:

(x, y) = (cos A, sin A), where A is the measurement of the angle.

In this case, $A = \frac{4 \pi}{3}$. Now, you can plug in A into (cos A, sin A) to find the x and y coordinates of the answer. Just make sure to set your calculator to radians, since $\frac{4 \pi}{3}$ is in radians.

Using this point $\left(x , y\right)$ on unit circle corresponding to $\frac{4 \pi}{3}$ is $\left(\cos \left(\frac{4 \pi}{3}\right) , \sin \left(\frac{4 \pi}{3}\right)\right)$ i.e. $\left(- \frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$

I hope that helps!