1. **State the problem:** Find the exact value of $\sec^{-1}(1)$ in radians. 2. **Recall the definition:** The inverse secant function $\sec^{-1}(x)$ gives the angle $\theta$ such that $\sec(\theta) = x$. 3. **Use the relationship:** Since $\sec(\theta) = \frac{1}{\cos(\theta)}$, we want to find $\theta$ such that $\frac{1}{\cos(\theta)} = 1$. 4. **Solve for $\cos(\theta)$:** $$\frac{1}{\cos(\theta)} = 1 \implies \cos(\theta) = 1$$ 5. **Find the angle:** The cosine of $\theta$ equals 1 at $\theta = 0$ radians within the principal range of $\sec^{-1}$, which is $[0, \pi]$ excluding $\frac{\pi}{2}$. 6. **Conclusion:** Therefore, $$\sec^{-1}(1) = 0$$ This is the exact value in radians.