Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions - 6.5 Assess Your Understanding - Page 418: 43

Answer

$\frac{6\sqrt3}{\pi}$

Work Step by Step

The general formula for average rate of change from $x$ to $y$ is $\frac{f(y)-f(x)}{y-x}.$ Hence here: $\frac{\tan{(2\cdot \frac{\pi}{6})}-\tan{(2\cdot0)}}{\frac{\pi}{6}-0} \\=\frac{\tan{\frac{\pi}{3}}-\tan{0}}{\frac{\pi}{6}} \\=\frac{\sqrt3-0}{\frac{\pi}{6}} \\=\frac{6\sqrt3}{\pi}$
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