Answer
$(\frac{1}{2}, \frac{\sqrt 3}{2})$
Work Step by Step
1. The terminal point determined by $\frac{\pi}{6}$ is $(\frac{\sqrt 3}{2}, \frac{1}{2})$
2. Base on the symmetry shown in the figure of the problem, the terminal point of $\frac{\pi}{3}$ is a mirror
point of $\frac{\pi}{6}$ around $y=x$
3. Use the same concept of inverse function, we can obtain the coordinates of $t=\frac{\pi}{3}$ by switching
$x,y$ from those of the $t=\frac{\pi}{6}$ which gives the terminal point determined by $\frac{\pi}{3}$ as $(\frac{1}{2}, \frac{\sqrt 3}{2})$
