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 603: 43


The domain of $x$ is $x\geq 1$.

Work Step by Step

From trigonometric identity we have $\sec^2 t-\tan^2 t=1$. Since $x=\sec t$ and $y=\tan t$, we obtain $x^2-y^2=1$. So, $y=\pm \sqrt{x^2-1}$. For the interval $0\leq t1$. Hence, the domain of $x$ is $x\geq 1$.
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