Explanation Given information : The parametric equation of the curve is x = 2 sin θ , y = 2 cos θ , and ( 0< t <2π ) , Formula used : We eliminate the parameter from the parametric equations x = f 1 ( t ) , y = f 2 ( t ) , and sketch the graph in x - y plane. Calculations: The parametric form of the curve is x = 2 sin θ ... (1) y = 2 cos θ ... (2) We find range of variable x, and yas ( 0 ≤ θ ≤ 2π ) .We see, ( 0 < θ < 2 π ) ⇒ − 2 ≤ 2 sin θ ≤ 2 ⇒ -2 ≤ x ≤ 2 ... (3) ( 0 ≤ θ ≤ 2 π ) ⇒ -2 ≤ 2 cos θ ≤ 2 ⇒ -2 ≤ y ≤ 2

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 9.5, Problem 30PS

To determine

Tofind:An explicit relationship between x and y from the equations x=f1(t) , y=f2(t) by elimination the parameter and sketch the path described by parametric equations over the interval.

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Chapter 9.5, Problem 29PS

Chapter 9.5, Problem 31PS

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Chapter 9 Solutions

Calculus

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Tofind: An explicit relationship between x and y from the equations x = f 1 ( t ) , y = f 2 ( t ) by elimination the parameter and sketch the path described by parametric equations over the interval.

Solution Summary: The author explains the parametric form of the curve, a complete circle with center at origin and radius of 2 units.

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Tofind:An explicit relationship between x and y from the equations x=f1(t) , y=f2(t) by elimination the parameter and sketch the path described by parametric equations over the interval.

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Chapter 9 Solutions