Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Additional and Advanced Exercises - Page 39: 17


See explanations.

Work Step by Step

Step 1. Calculate the area of the triangle $\Delta ABE$: $A_1=\frac{1}{2}AE\times BE=\frac{1}{2}cos\theta\times sin\theta$ Step 2. Calculate the area of the section with angle $\theta$: $A_2=\frac{1}{2}\times1^2\theta=\frac{\theta}{2}$ Step 3. Calculate the area of the triangle $\Delta ACD$: $A_3=\frac{1}{2}AD\times CD=\frac{1}{2}\times1\times tan\theta=\frac{1}{2} tan\theta=\frac{1}{2}\frac{sin\theta}{cos\theta}$ Step 4. Because $A_1\lt A_2\lt A_3$, we have: $\frac{1}{2}cos\theta\cdot sin\theta\lt \frac{\theta}{2}\lt \frac{1}{2}\frac{sin\theta}{cos\theta}$
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.