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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 43 (page 451)

Find the exact value of each expression. Do not use a calculator.
$\tan^{- 1} [\tan \frac{4 蟺}{5}]$

Short Answer

Expert verified

The value for the given expression

\tan^{- 1} [\tan \frac{4 蟺}{5}] = - \frac{蟺}{5}

Step by step solution

01

Step 1. Given Information

Given trigonometric expression

$\tan^{- 1} [\tan \frac{4 蟺}{5}]$

02

Step 2. Calculation

The value for the given expression

$\tan^{- 1} [\tan x] = \{\begin{cases} x - \frac{蟺}{2} < x < \frac{蟺}{2} \\ x - 蟺 \frac{蟺}{2} < x < \frac{3 蟺}{2} \end{cases} \tan^{- 1} [\tan \frac{4 蟺}{5}] = \frac{4 蟺}{5} - 蟺 = - \frac{蟺}{5}$

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