Chapter 7 - Trigonometric Identities and Equations - 7.5 Inverse Circular Functions - 7.5 Exercises - Page 707: 4

Fill the blank with ... $(1, \displaystyle \frac{\pi}{4})$ ...

Work Step by Step

Inverse functions have graphs that are reflections of each other relative to the line y=x. This means if (a,b) is on the graph of one, then (b,a) is on the graph of the other. To make $\tan x$ a one-to-one function, we restricted its domain to $(-\displaystyle \frac{\pi}{2},\ \displaystyle \frac{\pi}{2})$ and $\displaystyle \frac{\pi}{4}\in(-\frac{\pi}{2},\ \displaystyle \frac{\pi}{2})$, so $\displaystyle \frac{\pi}{4}$will be in the range of its inverse.

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