The problem you're working on asks for the exact value of the expression:

$\sin\left(\frac{\pi}{2}\right)$

The sine function, $\sin(\theta)$, relates to the unit circle. For $\theta = \frac{\pi}{2}$, we are at the point $(0, 1)$ on the unit circle.

So, the value of $\sin\left(\frac{\pi}{2}\right)$ is:

$\boxed{1}$

This is because the sine of an angle in the unit circle corresponds to the y-coordinate, and at $\frac{\pi}{2}$, the y-coordinate is 1.

Would you like a more detailed explanation of this concept? Here are 5 related questions to deepen your understanding:

1. What is the value of $\sin(0)$?
2. How do the values of sine change as the angle increases from $0$ to $\pi$?
3. What is the cosine of $\frac{\pi}{2}$?
4. Can you explain the unit circle and how trigonometric functions are derived from it?
5. How can you find the sine of angles greater than $2\pi$?

Tip: The sine function is periodic, repeating every $2\pi$, so you can use it to calculate sine values for any angle, positive or negative!