Explanation Given information : The parametric equation of the curve is x =1+sin t , y =- 2 + cos t , and ( 0 ≤ t ≤ 2 π ) , Formula used : We eliminate 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 =1+sin t .............(1) y =- 2 + cos t .............(2) We find the ranges of variablesx ,and y when ( 0 ≤ t ≤ 2π ) .We have ( 0 ≤ t ≤ 2π ) ⇒ 0 ≤ 1+sin t ≤ 0 ⇒ 1 ≤ x ≤ 1 .............(3) ( 0 < t < 2 π ) ⇒ -1 ≤ -2+cos t ≤ -3 ⇒ -1 ≤ y ≤ -1 .............(4) Now, we eliminate the parameter between x and y as follows: From equations (1), and (2), we have sin t = x -1 ⇒ si n 2 t = ( x -1 ) 2 y =- 2 + cos t ⇒ cos t = ( y + 2 ) ⇒ cos 2 t = ( y + 2 ) 2 Now, si n 2 t + cos 2 t = ( x -1 ) 2 + ( y + 2 ) 2 &e

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

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

Publisher: Kendall Hunt Publishing

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Chapter 9.5, Problem 31PS

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

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Chapter 9.5, Problem 30PS

Chapter 9.5, Problem 32PS

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4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to indicate the orientation of the graph. YA 10 x=4+cos(0) , y=-1+sin(0) -9 -8-7 -6 -5 4-3 -2 -10 4 56 7 8 9 10 х -1 -2 -3 -5 -6 -7 -9

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Chapter 9 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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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 of the parameter and sketch the path described by parametric equations over the given interval.

Solution Summary: The author calculates the parametric form of the curve by eliminating parameter and sketching the graph in x - y plane.

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

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