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 - Preliminary Questions - Page 602: 4

Answer

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Work Step by Step

In the parametric curve $ (t,\sin t)$ we have $x = t $ and $y = \sin t$, therefore, $y = sin x$. That is, the curve can be represented as a graph of a function. But in the parametric curve $ (\sin t,t)$ we have $x = \sin t $ and $y = t$, therefore, $x = sin y$. This equation does not define $y $ as a function of $x$, therefore the parametric curve $ (\sin t,t)$ cannot be represented as a graph of a function $y = f (x)$.
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