To determine $\sin 45^\circ$, we refer to the unit circle diagram provided in the image.

From the diagram, the coordinates for the point at $45^\circ$ are: $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ In the unit circle, the sine of an angle corresponds to the $y$-coordinate of the point. Therefore, we have:

$\sin 45^\circ = \frac{\sqrt{2}}{2}$

Would you like a more detailed explanation? Here are some related questions:

1. What is $\cos 45^\circ$ based on the unit circle?
2. How do you derive the coordinates for 30°, 45°, and 60° on the unit circle?
3. Why is the unit circle useful in trigonometry?
4. What is the sine of 30° and 60°, and how do they relate to $\sin 45^\circ$?
5. How can you use the Pythagorean identity to verify $\sin 45^\circ$ and $\cos 45^\circ$?

Tip: The unit circle helps visualize trigonometric values and makes it easier to remember key angles and their sine, cosine, and tangent values.