Explanation Given: Curve = r ( θ ) = R 〈 cos θ , sin θ 〉 = 〈 R cos θ , R sin θ 〉 Formula used: Tangent vector = T( θ ) = r ' ( θ ) | | r ' ( θ ) | | Normal vector = N( θ ) = T ' ( θ ) | | T ' ( θ ) | | Calculation: First we need to find tangent vector before finding normal vector. Tangent vector = T( θ ) = r ' ( θ ) | | r ' ( θ ) | | Now, r ' ( θ ) = 〈 − R sin θ , R cos θ 〉 ⇒ | | r ' ( θ ) | | = ( − R sin θ ) 2 + ( R cos θ ) 2 = R 2 sin 2 θ + R 2 cos 2 θ = R 2 ( sin 2 θ + cos 2 θ ) = R 2 ( 1 ) = R ∴ T( θ ) = r ' ( θ ) | | r ' ( θ ) | | = 〈 − R sin θ , R cos θ 〉 R = 〈 − sin θ , cos θ 〉 Normal vector = N( θ ) = T ' ( θ ) | | T ' ( θ ) | |

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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 13.4, Problem 36E

To determine

The normal vector of curve r(θ)=R〈cosθ,sinθ〉 and draw it at when θ=π4 with R=4.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 35E

Chapter 13.4, Problem 37E

Students have asked these similar questions

4. Suppose that the population of a certain collection of rare Brazilian ants is given by P(t)=(t+100) In(t+2), Where t represents the time in days. Find and interpret the rates of change of the population on the third day and on the tenth day.

Find all values of x for f (x)=(x²-4) 4 where the tangent line is horizontal. 5. Find the slope of the tangent line to the graph of f(x)=-√8x+1 at x=1. Write the equation of the tangent line.

3. Find the derivative of each function. Label with appropriate derivative notation showing both dependent and independent variables. f(t)=4t(2t⭑+4)³ a. f(t)=4t (2t+4)³ (Answer must be factored.) b. y= 3 1 (2x³-4) 6

Chapter 13 Solutions

Calculus: Early Transcendentals

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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 normal vector of curve r ( θ ) = R 〈 cos θ , sin θ 〉 and draw it at when θ = π 4 with R = 4 .

Solution Summary: The author explains that the normal vector of curve r(theta )=Rlangle

Concept explainers

The normal vector of curve r(θ)=R〈cosθ,sinθ〉 and draw it at when θ=π4 with R=4.

Want to see the full answer?

Chapter 13 Solutions