Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 744: 106


The statement makes sense.

Work Step by Step

When we convert an equation from polar form to rectangular form, then the obtained rectangular equation may not define y as a function of x. For example, let us consider the polar equation $\theta =0$. Its rectangular equation is given by $\begin{align} & \tan \theta =\frac{y}{x} \\ & y=x\tan \theta \\ & y=x\left( 0 \right) \\ & =0 \end{align}$ This rectangular equation is $y=0$ From the equation, we can see that after conversion from polar form to rectangular form the rectangular equation has not defined y as a function of x.
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