Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.1 - The Unit Circle - 5.1 Exercises - Page 408: 38

Answer

a. $\overline{t}=0$ b. $\displaystyle \overline{t}=\frac{\pi}{4}$ c. $\displaystyle \overline{t}=\frac{\pi}{6}$ d. $\overline{t}=4-\pi\approx 0.86$

Work Step by Step

The reference number associated with the real number $t$ is the shortest distance along the unit circle between the terminal point determined by $t$ and the x-axis. For each t, find each terminal point on the unit circle (positive=counterclockwise) and associate it with the terminal point of some t between 0 and $ 2\pi$ If the terminal point "lands" in quadrants II, III or IV, choose the symmetric terminal number ($\pm\pi$) in quadrant I$:$ t in Q.II $\Rightarrow \overline{t}=\pi-t$ t in Q.III$\Rightarrow \overline{t}=t-\pi$ t in Q.IV$\Rightarrow \overline{t}=2\pi-t$ ------------------- a. $ t=9\pi$ has the same terminal point as $\pi$, its reference number is $\pi-\pi=0$ b. $ \displaystyle \frac{-5\pi}{4}$ (clockwise from 0), has the same terminal point as$ \displaystyle \frac{3\pi}{4}$ ( in Q.II ) its reference number is $\displaystyle \pi-\frac{3\pi}{4}=\frac{\pi}{4} $ c. The terminal point of $t=\displaystyle \frac{25\pi}{6}=4\pi+\frac{\pi}{6}$ is the same terminal point as $\displaystyle \frac{\pi}{6}$ (Q.I), its reference number is $\displaystyle \frac{\pi}{6}$ d. The terminal point of 4 is in Q.III, ($\pi\approx$3.14), its reference number is $4-\pi\approx 4-3.14=0.86$
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.