1. **State the problem:** We need to understand the angle $\frac{5\pi}{4}$ radians on the unit circle and its position. 2. **Recall the unit circle basics:** The unit circle has radius 1 and is centered at $(0,0)$. Angles are measured in radians from the positive x-axis counterclockwise. 3. **Interpret the angle $\frac{5\pi}{4}$:** - $\pi$ radians is half a circle (180 degrees). - $\frac{5\pi}{4} = \pi + \frac{\pi}{4}$ means starting at $\pi$ (180 degrees) and moving an additional $\frac{\pi}{4}$ (45 degrees). 4. **Locate the angle on the circle:** - $\pi$ radians points to $(-1,0)$ on the unit circle. - Adding $\frac{\pi}{4}$ moves the point into the third quadrant. 5. **Coordinates of the point:** - The coordinates for angle $\theta$ on the unit circle are $(\cos \theta, \sin \theta)$. - For $\theta = \frac{5\pi}{4}$: $$\cos \frac{5\pi}{4} = -\frac{\sqrt{2}}{2}, \quad \sin \frac{5\pi}{4} = -\frac{\sqrt{2}}{2}$$ 6. **Summary:** The angle $\frac{5\pi}{4}$ radians corresponds to the point $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$ in the third quadrant of the unit circle. This explains the position of the label $\frac{5\pi}{4}$ near the top-left of the image, indicating the angle's terminal side.