Explanation Given : The given polar curve r = 1 + c sin θ . Calculation: Calculate the value of x . x = r cos θ Substitute 1 + c sin θ for r in the above equation. x = r cos θ x = ( 1 + c sin θ ) cos θ = cos θ + c sin θ cos θ Substitute 1 2 sin 2 θ for sin θ cos θ in the above equation. x = cos θ + c sin θ cos θ x = cos θ + c ( 1 2 sin 2 θ ) Calculate the value of y . y = r sin θ Substitute 1 + c sin θ for r in the above equation. y = r sin θ y = ( 1 + c sin θ ) sin θ y = sin θ + c sin 2 θ Use online graphing calculator and sketch the graph of the polar curve r = 1 + c sin θ with different values of c and θ as shown below in Figure 1. From Figure 1, it is observed that the y values lies between − 1 and 2. Calculate the smallest viewing rectangle as follows. x = cos θ + c ( 1 2 sin 2 θ ) Here, sin 2 θ ≥ 0 when 0 ≤ θ ≤ π 2 and sin 2 θ ≤ 0 when − π 2 ≤ θ ≤ 0 . So, for − π 2 ≤ θ ≤ 0 , x has a maximum value when c = 0 . Substitute 0 for c in the above equation. x = cos θ + c ( 1 2 sin 2 θ ) x = cos θ So, the maximum value of x will be 1, which is happen when θ = 0 . That is, the maximum value occurs only in the interval [ 0 , π 2 ]

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 10, Problem 3P

To determine

The different rectangle curves from the given polar equation and smallest viewing rectangle that contains every member of the family of polar curves.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10, Problem 2P

Chapter 10, Problem 4P

Students have asked these similar questions

2) Drive the frequency responses of the following rotor system with Non-Symmetric Stator. The system contains both external and internal damping. Show that the system loses the reciprocity property.

1) Show that the force response of a MDOF system with general damping can be written as: X liax) -Σ = ral iw-s, + {0} iw-s,

3) Prove that in extracting real mode ø, from a complex measured mode o, by maximizing the function: maz | ቀÇቃ | ||.|| ||.||2 is equivalent to the solution obtained from the followings: max Real(e)||2

Chapter 10 Solutions

Calculus: Early Transcendentals

Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Sketch the curve by using the parametric equations...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.

The different rectangle curves from the given polar equation and smallest viewing rectangle that contains every member of the family of polar curves.

Solution Summary: The author explains the different rectangle curves from the given polar equation and smallest viewing rectangle that contains every member of the family of

Videos

The different rectangle curves from the given polar equation and smallest viewing rectangle that contains every member of the family of polar curves.

Want to see the full answer?

Chapter 10 Solutions