Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.1 Exercises - Page 665: 17

Answer

Cartesian equation: $y^2 - x^2 = 1, y \geq 1$ --------------
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Work Step by Step

(a) $x =sinh \space t$ $x^2 = sinh^2 \space t$ $-x^2 = -sinh^2 \space t$ $y =cosh \space t$ $y^2 = cosh^2 \space t$ Adding both equations: $y^2 - x^2 = cosh^2t-sinh^2t$ $y^2 - x^2 = 1$ - Notice, the parametric equation is only valid for $y \geq 1$, since $cosh \space t$ has a minimum value of $1$. Therefore, the cartesian equation should also have this condition: $y^2 - x^2 = 1, y \geq 1$ ----- (b) 1. Plot points determined by values for $t$. I used -3, -2, -1, 0, 1, 2 and 3. 2. Join them to produce a curve. 3. Draw an arrow indicating which direction the curve goes from $t = -3$ to $t= 3$
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