1. The problem asks for the value of $\arctan(1)$, which is the angle whose tangent is 1. 2. Recall the definition: $\arctan(x)$ is the inverse function of $\tan(\theta)$, so $\arctan(1)$ means find $\theta$ such that $\tan(\theta) = 1$. 3. Important rule: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. When $\tan(\theta) = 1$, it means $\sin(\theta) = \cos(\theta)$. 4. The angle where sine and cosine are equal in the principal range of $\arctan$ (which is $(-\frac{\pi}{2}, \frac{\pi}{2})$) is $\theta = \frac{\pi}{4}$ radians. 5. Therefore, $\arctan(1) = \frac{\pi}{4}$. 6. Among the options given, option b. $\frac{\pi}{4}$ is correct. Final answer: $\boxed{\frac{\pi}{4}}$