Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 680: 3

Answer

The exact value of the trigonometric function $\tan 2\theta $ is $\frac{24}{7}$.

Work Step by Step

The figure shows the right-angle triangle. In this triangle, the base is $4$, the perpendicular is $3$, and the hypotenuse is $5$. Calculate the value of $\tan 2\theta $. Recall the double angle formula. $\begin{align} & \tan 2\theta =\frac{2\tan \theta }{1-{{\tan }^{2}}\theta } \\ & =\frac{2\left( \frac{\text{perpendicular}}{\text{base}} \right)}{1-{{\left( \frac{\text{perpendicular}}{\text{base}} \right)}^{2}}} \end{align}$ Substitute $4$ for the base and $3$ for the perpendicular. $\begin{align} & \tan 2\theta =\frac{2\left( \frac{\text{3}}{\text{4}} \right)}{1-{{\left( \frac{\text{3}}{\text{4}} \right)}^{2}}} \\ & =\frac{2\left( \frac{\text{3}}{\text{4}} \right)}{1-\frac{9}{16}} \\ & =\frac{\frac{\text{3}}{\text{2}}}{\frac{7}{16}} \\ & =\frac{24}{7} \end{align}$ Therefore, the exact value of the trigonometric function $\tan 2\theta $ is $\frac{24}{7}$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.