Find the value of $\alpha$ given that $\sin{\alpha} = 1$.

1. Problem Description

Find the value of $\alpha$ given that $\sin{\alpha} = 1$.

2. Solution Steps

We are given the equation $\sin{\alpha} = 1$. We need to find the value of $\alpha$.

We know that the sine function achieves a value of 1 at $\frac{\pi}{2}$ radians (or 90 degrees).

Also, since the sine function is periodic with a period of $2\pi$, we can add multiples of $2\pi$ to our initial solution to get other possible solutions.

Therefore, $\alpha = \frac{\pi}{2} + 2n\pi$, where $n$ is an integer.

However, the question is likely expecting the smallest positive value of $\alpha$.

Thus, we can let $n = 0$, which gives $\alpha = \frac{\pi}{2}$.

3. Final Answer

$\alpha = \frac{\pi}{2}$