Explanation Given information : f is a differential function of θ . Formula used: The relation between the polar coordinates and the Cartesian coordinates is given by x = r c o s θ y = r s i n θ Proof: The relation between the polar coordinates and the Cartesian coordinates is given by x = r c o s θ y = r s i n θ Since r = f ( θ ) , x = f ( θ ) c o s θ y = f ( θ ) s i n θ } ......(1) Differentiating (1), with respect to ‘ θ ’, we have d x d θ = f ' ( θ ) c o s θ − f ( θ ) s i n θ d y d θ = f ' ( θ ) sin θ + f (<

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.3, Problem 57PS

To determine

To prove:The tangent line to the polar curve r=f(θ) at the point P(r,θ) has slope

m=f(θ)cosθ+f'(θ)sinθ−f(θ)sinθ+f'(θ)cosθ , whenever the denominator is not zero.

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Chapter 6.3, Problem 56PS

Chapter 6.3, Problem 58PS

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Chapter 6 Solutions

Calculus

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To prove: The tangent line to the polar curve r = f ( θ ) at the point P ( r , θ ) has slope m = f ( θ ) c o s θ + f ' ( θ ) s i n θ − f ( θ ) sin θ + f ' ( θ ) c o s θ , whenever the denominator is not zero.

Solution Summary: The author explains that the tangent line r=f(theta ) has a slope and the relation between polar and Cartesian coordinates is given.

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To prove:The tangent line to the polar curve r=f(θ) at the point P(r,θ) has slope

m=f(θ)cosθ+f'(θ)sinθ−f(θ)sinθ+f'(θ)cosθ , whenever the denominator is not zero.

Want to see the full answer?

Chapter 6 Solutions

To prove: The tangent line to the polar curve r = f ( θ ) at the point P ( r , θ ) has slope m = f ( θ ) c o s θ + f ' ( θ ) s i n θ − f ( θ ) sin θ + f ' ( θ ) c o s θ , whenever the denominator is not zero.

Solution Summary: The author explains that the tangent line r=f(theta ) has a slope and the relation between polar and Cartesian coordinates is given.

Videos

To prove:The tangent line to the polar curve r=f(θ) at the point P(r,θ) has slope m=f(θ)cosθ+f'(θ)sinθ−f(θ)sinθ+f'(θ)cosθ , whenever the denominator is not zero.

Want to see the full answer?

Chapter 6 Solutions

To prove:The tangent line to the polar curve r=f(θ) at the point P(r,θ) has slope

m=f(θ)cosθ+f'(θ)sinθ−f(θ)sinθ+f'(θ)cosθ , whenever the denominator is not zero.