What are coordinates of the terminal point determined by t = 20 pi /3

The terminal point determined by an angle is given by the point on the circumference of the unit circle such that the angle between the radius of the circle and the x-axis is the given angle.

Given the angle

This angle is equivalent to the angle


To find the terminal point, we note that the radius of the unit circle at that point makes a right angle with the coordinates of the terminal point.
We also note that angle is on the 2nd quadrant of the coordinate axis. This means that the x-value of the terminal point is negative while the y-value is positive.
We also note that the radius of a unit circle is 1.

To find the x-coordinate of the terminal point, we use the relation


Similarly to find the y-coordinate of the terminal point, we use the relation


Therefore, the coordinates of the terminal point determined by T = 20 pi /3 are