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: 52


$$ \frac{d y}{d x}= \frac{-3\sin3\theta}{2\cos 2\theta} $$ and at $\theta=\pi/6$, we have $$ \frac{d y}{d x}=-3. $$

Work Step by Step

Since $x=\sin 2\theta $ and $y=\cos 3\theta$ then we have $$ \frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{-3\sin3\theta}{2\cos 2\theta} $$ and at $\theta=\pi/6$, we have $$ \frac{d y}{d x}=- \frac{3}{2(1/2)}=-3. $$
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