1. **Problem:** Find the coordinates of the point on the unit circle corresponding to an angle of $\frac{\pi}{3}$ radians. 2. **Formula and rules:** The unit circle is a circle with radius 1 centered at the origin $(0,0)$ in the coordinate plane. Any point on the unit circle corresponding to an angle $\theta$ (measured in radians from the positive x-axis) has coordinates $(\cos \theta, \sin \theta)$. 3. **Step-by-step solution:** - Given $\theta = \frac{\pi}{3}$. - Calculate $\cos \frac{\pi}{3}$ and $\sin \frac{\pi}{3}$. 4. **Evaluate:** - $\cos \frac{\pi}{3} = \frac{1}{2}$. - $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$. 5. **Answer:** The coordinates of the point on the unit circle at angle $\frac{\pi}{3}$ are $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$. This means if you start at the point $(1,0)$ on the unit circle and rotate counterclockwise by $\frac{\pi}{3}$ radians, you reach the point $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ on the circle.