Explanation Given info: Parametric equation of curve ( 2 t 2 − 7 , t , 9 − t 2 ) ( 2 t 2 − 7 , t , − 9 − t 2 ) , where − 3 ≤ t ≤ 3 Concept used: If − a ≤ t ≤ 3 , then you can assume t = a Cos θ , θ ∈ R Put the value of t in each parametric equation you get. Calculation: − 3 ≤ t ≤ 3 Let t = 3 Cos θ then Cos θ varies between − 1 to 1 it means that t varies from − 3 to 3 . Put t = 3 Cos θ in each parametric equation ( 2 t 2 − 7 , t , ± 9 − t 2 ) ( 2 ( 3 Cos θ ) 2 − 7 , 3Cos θ , ± 9 − ( 3 Cos θ ) 2 ) ( 18 Cos 2 θ − 7 , 3Cos θ , ± 9 ( 1 − Cos 2 θ ) ) = ( 9 ( 2 Cos 2 θ ) ȡ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.1, Problem 30E

To determine

Find a parameterization of the curve in exercise $25$ . Using trigonometric function.

$x = 2 t^{2} - 7, y = t, z = \pm \sqrt{9 - t^{2}} where - 3 \leq t \leq 3$

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Chapter 14.1, Problem 29E

Chapter 14.1, Problem 31E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Find a parameterization of the curve in exercise 25 . Using trigonometric function. x = 2 t 2 − 7 , y = t , z = ± 9 − t 2 where − 3 ≤ t ≤ 3

Solution Summary: The author explains how two parametric equations can be replaced by a 'parametric equation' using trigonometric function.

Videos

Find a parameterization of the curve in exercise $25$ . Using trigonometric function.

$x = 2 t^{2} - 7, y = t, z = \pm \sqrt{9 - t^{2}} where - 3 \leq t \leq 3$

Want to see the full answer?

Chapter 14 Solutions

Find a parameterization of the curve in exercise 25 . Using trigonometric function. x = 2 t 2 − 7 , y = t , z = ± 9 − t 2 where − 3 ≤ t ≤ 3

Solution Summary: The author explains how two parametric equations can be replaced by a 'parametric equation' using trigonometric function.

Videos

Find a parameterization of the curve in exercise 25. Using trigonometric function. x=2t2−7, y=t, z=±9−t2 where −3≤t≤3

Want to see the full answer?

Chapter 14 Solutions

Find a parameterization of the curve in exercise $25$ . Using trigonometric function.

$x = 2 t^{2} - 7, y = t, z = \pm \sqrt{9 - t^{2}} where - 3 \leq t \leq 3$