1. The problem is to find the value of $\sin^{-1}(1)$ without using a calculator. 2. The function $\sin^{-1}(x)$, also called arcsine, gives the angle whose sine is $x$. 3. We need to find an angle $\theta$ such that $\sin(\theta) = 1$. 4. Recall that sine of $\frac{\pi}{2}$ (or 90 degrees) is 1, i.e., $\sin\left(\frac{\pi}{2}\right) = 1$. 5. Since the range of $\sin^{-1}(x)$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, the angle $\theta = \frac{\pi}{2}$ is the principal value. 6. Therefore, $\sin^{-1}(1) = \frac{\pi}{2}$. Final answer: $$\sin^{-1}(1) = \frac{\pi}{2}$$