The expression shown in the image is $\sin \left( \frac{\pi}{4} \right)$.

To evaluate $\sin \left( \frac{\pi}{4} \right)$, recall that:

$\sin \left( \frac{\pi}{4} \right) = \sin 45^\circ = \frac{\sqrt{2}}{2}$

Thus, the value of $\sin \left( \frac{\pi}{4} \right)$ is $\frac{\sqrt{2}}{2}$.

Would you like more details or further clarifications?

Here are some related questions you might find helpful:

1. How do you evaluate other trigonometric functions at common angles?
2. What are the values of sine, cosine, and tangent for $\frac{\pi}{6}$ and $\frac{\pi}{3}$?
3. Can you explain how to derive the exact value of $\sin \left( \frac{\pi}{4} \right)$ geometrically?
4. How does the unit circle help in determining trigonometric values?
5. What are the key differences between sine and cosine functions in terms of symmetry?

Tip: Memorizing the values of sine, cosine, and tangent for standard angles like $30^\circ, 45^\circ,$ and $60^\circ$ can simplify many trigonometric calculations.