Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 53


$$ \frac{d y}{d x}= -\frac{1}{3\sin \theta \cos \theta} $$ and at $\theta=\pi/4$, we have $$ \frac{d y}{d x}=-\frac{2}{3}. $$

Work Step by Step

Since $x=\sin^3\theta $ and $y=\cos \theta$, then we have $$ \frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{- \sin\theta}{3\sin^2 \theta \cos \theta}=-\frac{1}{3\sin \theta \cos \theta} $$ and at $\theta=\pi/4$, we have $$ \frac{d y}{d x}=- \frac{1}{3(1/2)}=-\frac{2}{3}. $$
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.