Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.1 Polar Cordinates - 8.1 Assess Your Understanding - Page 592: 64


$(2.25, 4.35)$

Work Step by Step

Solve for $r$ using the formula $r=\sqrt {x^{2}+y^{2}}$ to obtain: $$r=\sqrt {(-0.8)^{2}+(-2.1)^{2}}=2.25$$ Use the formula $\alpha=\tan^{-1}(\frac{y}{x})$ to find the reference angle: $$\alpha=\tan^{-1}\left(\frac{-2.1}{-0.8}\right)=1.21$$ Since $(-0.8,-2.1)$ is in the third quadrant, then $$\theta=\alpha+\pi=1.21+3.14=4.35$$ Thus, the polar coordinates for the point $(-0.8,-2.1)$ is $(2.25, 4.35)$.
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.