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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!

Find the exact value of the following expression: sin(π/2).

Learn how to find the exact value of sin(π/2) using the unit circle. This trigonometry problem covers key concepts like the sine function and its relationship to the y-coordinate on the unit circle. Ideal for high school students in Grades 9-12.

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