## Precalculus (6th Edition) Blitzer

The exact value of the provided expression is ${{\tan }^{-1}}1=\frac{\pi }{4}$.
Let us assume, $\theta ={{\tan }^{-1}}1$. Then, $\tan \theta =1$ For the tan function, the interval for the angle is $\left( \frac{-\pi }{2},\frac{\pi }{2} \right)$. Therefore, the only angle that satisfies $\tan \theta =1$ is $\frac{\pi }{4}$. Thus, $\theta =\frac{\pi }{4}$ and the exact value of the given expression is: ${{\tan }^{-1}}1=\frac{\pi }{4}$