To solve the equation \(\sin x = 1\), we need to determine the values of \(x\) where the sine function equals 1.

The sine function reaches the value of 1 at specific points on the unit circle. The general solution is:

\[
x = \frac{\pi}{2} + 2n\pi, \quad n \in \mathbb{Z}
\]

This represents all angles where \(\sin x = 1\), starting from \(\frac{\pi}{2}\) and repeating every full circle, which is \(2\pi\) radians.

### Key steps:
1. **Basic solution**: The sine of \(\frac{\pi}{2}\) is 1, so \(x = \frac{\pi}{2}\) is the primary solution.
2. **General solution**: Since sine is periodic, the solution repeats every \(2\pi\), giving \(x = \frac{\pi}{2} + 2n\pi\).

Would you like more details on the unit circle or sine function properties?

### Relative Questions:
1. What are the other key angles of the sine function?
2. How does the period of sine affect its solutions?
3. Can you explain how the sine function is derived from the unit circle?
4. How would the solution change if \(\sin x = -1\)?
5. What are the key characteristics of sine and cosine in trigonometry?

### Tip:
The sine function has a period of \(2\pi\), so its values repeat after every full rotation around the unit circle!

Learn how to solve the trigonometric equation sin(x) = 1. This step-by-step guide covers key trigonometric concepts, including the sine function and its periodicity, and provides a general solution for all values of x where sin(x) equals 1. Suitable for high school students in Grades 9-12.

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