Explanation Given data: The parametric equation for the variable x is as below. x = cos t (1) The parametric equation for the variable y is as below. y = sin t − sin c t (2) Calculation: The family of curve for the different values of c for the variable x is as below. The parametric equation for the variable x is as below. x = cos t The family of curve for the different values of c for the variable y is as below. The parametric equation for the variable y is as below. y = sin t − sin c t Substitute the value of 2 for c in equation (2). y = sin t − sin c t = sin t − sin ( 2 ) t y = sin t − sin 2 t Substitute 3 for c in equation (2). y = sin t − sin c t = sin t − sin ( 3 ) t y = sin t − sin 3 t Substitute 4 for c in equation (2). y = sin t − sin c t = sin t − sin ( 4 ) t y = sin t − sin 4 t Substitute 5 for c in equation (2). y = sin t − sin c t = sin t − sin ( 5 ) t y = sin t − sin 5 t Substitute 1 2 for c in equation (2). y = sin t − sin c t = sin t − sin ( 1 2 ) t y = sin t − sin 0.5 t Substitute 3 4 for c in equation (2). y = sin t − sin c t = sin t − sin ( 3 4 ) t y = sin t − sin 0.75 t Substitute 2 5 for c in equation (2). y = sin t − sin c t = sin t − sin ( 7 5 ) t y = sin t − sin 1.4 t Substitute 2.3 for c in equation (2). y = sin t − sin c t = sin t − sin ( 2.3 ) t y = sin t − sin 2.3 t Substitute 4.7 for c in equation (2). y = sin t − sin c t = sin t − sin ( 4.7 ) t y = sin t − sin 4.7 t Substitute 2.359 for c in equation (2). y = sin t − sin c t = sin t − sin ( 2.359 ) t y = sin t − sin 2.359 t Equations x = cos t and y = sin t − sin 2 t are used to obtain the values of x and y respectively. Substitute 0 for t in equation x = cos t . x = cos t = cos ( 0 ) x = 1 Substitute 0 for t in equation y = sin t − sin 2 t . y = sin t − sin 2 t = sin ( 0 ) − sin 2 ( 0 ) = 0 Repeat the calculation of x and y values using parametric equations x = cos t and y = sin t − sin 2 t for values of t ranging from 0 degree till 360 degrees. Form a set of 360 coordinate points for the curve and plot the curve as below. Graph: The graph is plotted for values of c = 2 . Equations x = cos t and y = sin t − sin 3 t are used to obtain the values of x and y respectively. Substitute 0 for t in equation x = cos t . x = cos t = cos ( 0 ) x = 1 Substitute 0 for t in equation y = sin t − sin 3 t . y = sin t − sin 3 t = sin ( 0 ) − sin 3 ( 0 ) = 0 Repeat the calculation of x and y values using parametric equations x = cos t and y = sin t − sin 3 t for values of t ranging from 0 degree till 360 degrees. Form a set of 360 coordinate points for the curve and plot the curve as below. Graph: The graph is plotted for values of c = 3 . Equations x = cos t and y = sin t − sin 4 t are used to obtain the value of x and y respectively Substitute 0 for t in equation x = cos t . x = cos t = cos ( 0 ) x = 1 Substitute 0 for t in equation y = sin t − sin 4 t . y = sin t − sin 4 t = sin ( 0 ) − sin 4 ( 0 ) y = 0 Repeat the calculation of x and y values using parametric equations x = cos t and y = sin t − sin 4 t for values of t ranging from 0 degree till 360 degrees. Form a set of 360 coordinate points for the curve and plot the curve as below. Graph: The graph is plotted for values of c = 4 . Equations x = cos t and y = sin t − sin 5 t are used to obtain the value of x and y respectively

Single Variable Calculus: Early Transcendentals

8th Edition

ISBN: 9781305270336

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 10.1, Problem 52E

To determine

To plot: The graph for members of family of curves using the parametric equations x=cost and y=sint−sinct.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.1, Problem 51E

Chapter 10.2, Problem 1E

Students have asked these similar questions

2. Find the Bezier surface equation using the 9 control points shown below. Use the u and v directions shown. It is required to show all the calculation processes for finding Bernstein polynomials. Find the surface tangent, twist and normal vectors at point u=0.5 and v=0.5. (40 points) y 10 9 8 7 6 5 4 3 2 Poo и 1 1 2 3 4 5 6 7 8 9 10 10 X

A cable runs along the wall from C to P at a cost of $24 per meter, and straight from P to M at a cost of $26 per meter. If M is 10 meters from the nearest point A on the wall where P lies, and A is 72 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost. C 72 P A 10 M

The number of bank robberies in a country for the years 2010-2018 is given in the following figure. Consider the closed interval [2010,2018]. (a) Give all relative maxima and minima and when they occur on the interval. (b) Give the absolute maxima and minima and when they occur on the interval. Incidents 7000- 6000-5 5482 5000- 4424 4273 4822 4000- 3708 3748 4229 4089 3000- 2582 2000- 1000- 0 2010 2012 2014 2016 2018 Year

Chapter 10 Solutions

Single Variable Calculus: Early Transcendentals

Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To plot: The graph for members of family of curves using the parametric equations x = cos t and y = sin t − sin c t .

Solution Summary: The author plots the graph for members of the family of curves using the parametric equations x=mathrmcost and

Concept explainers

To plot: The graph for members of family of curves using the parametric equations x=cost and y=sint−sinct.

Want to see the full answer?

Chapter 10 Solutions