Question

what are the coordinates of the terminal point determined by t= 10pi/3

Answer 1

So you are finding the point on the unit circle.
First, we see that 10pi/3 is more than 2pi, which is the 360 degree angle around a circle.
So we can subtract off 2pi to get 4pi/3.

Answer 2

So it is the same as finding the terminal point for 4pi/3.

Answer 3

I like to convert to degrees because it's easier for me.
4pi/3 * 180/pi degrees = 240 degrees.
So it's 180 degrees + 60 more.
We know both x and y are negative

Answer 4

Therefore I think the terminal point is (-1/2, -sqrt3/2)