As per given by the question,
There are given that the terminal point,
[tex]t=\frac{20\pi}{3}[/tex]
Now,
To find the terminal point, there are use the refrence point,
[tex]t=\frac{2\pi}{3}[/tex]
That means,
The given angle is equivalent to the angle ,
[tex]t=\frac{2\pi}{3}[/tex]
Now,
According to the terminal point concept,
The radius of the unit circle at that point makes a right angle with the coordinates of the terminal point and,
There is also noted that the given terminal is on the 2nd quadrant of the cpordinate axis.
So,
The x value of the terminal point is negative and y value is positive.
Then,
There is use the relation,
[tex]-\cos (\pi-\frac{2\pi}{3})=\frac{x}{1}[/tex]
Because the radius of the uit circle is 1.
Now,
[tex]\begin{gathered} -\cos (\pi-\frac{2\pi}{3})=\frac{x}{1} \\ -\text{cos(}\frac{\pi}{3})=x \\ x=-\frac{1}{2} \end{gathered}[/tex]
Then,
Similarly to find the y-coordinate.
So,
Here, find the y-coordinate to relate the sine trigonometric function.
[tex]\begin{gathered} \sin (\pi-\frac{2\pi}{3})=\frac{y}{1} \\ \sin (\frac{\pi}{3})=y \\ y=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]
The coordinate of the terminal point is,
[tex](x,\text{ y)=(-}\frac{1}{2},\text{ }\frac{\sqrt[]{3}}{2})[/tex]
Hence, the option A is correct.
