What is the coordinate point at (5pi )/(3) ((1)/(2),-(sqrt (3))/(2)) (-(1)/(2),(sqrt (3))/(2)) ((sqrt (3))/(2),-(1)/(2)) (sqrt (3) 1)

To find the coordinate point at $\frac{5\pi}{3}$, we need to determine the angle in standard position and then find the corresponding coordinates on the unit circle.<br /><br />Step 1: Determine the angle in standard position.<br />The angle $\frac{5\pi}{3}$ is equivalent to $300^\circ$ or $-60^\circ$ (since $360^\circ - 300^\circ = 60^\circ$).<br /><br />Step 2: Find the coordinates on the unit circle.<br />The coordinates on the unit circle for an angle of $300^\circ$ or $-60^\circ$ are $\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$.<br /><br />Therefore, the coordinate point at $\frac{5\pi}{3}$ is $\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$.