The coordinates given in the problem are $\left( \frac{\sqrt{3}}{2}, -\frac{1}{2} \right)$. These coordinates correspond to a point on the unit circle.

To determine the angle, we note that:

• $\frac{\sqrt{3}}{2}$ is the $x$-coordinate.
• $-\frac{1}{2}$ is the $y$-coordinate.

This point is in the fourth quadrant of the unit circle, where the cosine value (related to the $x$-coordinate) is positive, and the sine value (related to the $y$-coordinate) is negative.

In the first quadrant, the point $\left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right)$ corresponds to an angle of $30^\circ$ or $\frac{\pi}{6}$. Since we are in the fourth quadrant, the angle is $360^\circ - 30^\circ = 330^\circ$ (or $2\pi - \frac{\pi}{6} = \frac{11\pi}{6}$ radians).

Thus, the angle at the position $\left( \frac{\sqrt{3}}{2}, -\frac{1}{2} \right)$ is 330° (or $\frac{11\pi}{6}$).

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you determine angles in other quadrants using the unit circle?
2. What is the relationship between radians and degrees?
3. How do you convert an angle from degrees to radians?
4. What are the sine and cosine values for common angles like $30^\circ$, $45^\circ$, and $60^\circ$?
5. How do you find the reference angle for a given angle on the unit circle?

Tip: Knowing key points on the unit circle makes it easier to find angles based on coordinates.