The coordinates for the point on the unit circle are:
(-1/2, - (√3)/2)
How to get the coordinates of the point?
Remember that for a point on the unit circle that defines an angle θ, the coordinates of the point are given by:
tan(θ) = y/x
Such that:
√(x^2 + y^2) = 1
Then we have two equations to work with.
In this case, θ = (4/3)*pi
Replacing that in the first equation, and solving for y, we get:
tan((4/3)*pi)*x = y
(√3)*x = y
Now we can replace that on the other equation:
√(x^2 + y^2) = 1
√(x^2 + ((√3)*x)^2) = 1
√(x^2 + 3x^2) = 1
√(4*x^2) = 1
±2x = 1
x = ±1/2
Then:
y = (√3)*x = ±(√3)/2
But notice that our point is on the third quadrant, so both of the values for the components must be the negative ones.
Finally, the coordinates are:
(-1/2, - (√3)/2)
If you want to learn more about unit circles, you can read: