Chapter 5 - Section 5.5 - Inverse Trigonometric Functions and Their Graphs - 5.5 Exercises - Page 445: 7

a) $-\frac{\pi}{4}$ b) $\frac{\pi}{3}$ c) $\frac{\pi}{6}$

a) First, we look at the interval of the inverse of tangent which is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a slope of $-1$ in that interval. The answer is $-\frac{\pi}{4}$ b) First, we look at the interval of the inverse of tangent which is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a slope of $\sqrt3$ in that interval. The answer is $\frac{\pi}{3}$ c) First, we look at the interval of the inverse of tangent which is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a slope of $-1$ in that interval. The answer is $\frac{\pi}{6}$