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CalculusCalculus10th Edition

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Chapter 10.4, Problem 105E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Problem 98E
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Problem 100E
Problem 101E
Problem 102E
Problem 103E
Problem 104E
Problem 105E
Problem 106E
Problem 107E
Problem 108E
Problem 109E
Problem 110E
Problem 111E
Problem 112E
Problem 113E
Problem 114E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Finding an Angle In Exercises 107-112, use the result of Exercise 106 to find the angle ψ

between the radial and tangent lines to the graph for the indicated value of θ

. Use a graphing utility to graph the polar equation, the radial line, and the tangent line for the indicated value of θ

. Identify the angle ψ .

Polar Equation Value of θ

r = 2 ( 1 − cos θ )

θ = π

To determine

To calculate: The angle ψ between the radial and tangent line for the polar equation r=2(1−cosθ) at θ=π and then sketch its graph with the help of graphing utility along with its radial and tangent line.

Explanation

Given:

The polar equation is given as r=2(1−cosθ) at θ=π.

Formula used:

The angle ψ between the radial and tangent line to the graph for the polar equation r=f(θ) is given by,

tanψ=rdrdθ

Calculation:

Consider the polar equation, r=2(1−cosθ)

Differentiate r with respect to θ,

drdθ=ddθ(2(1−cosθ))=ddθ(2−2cosθ)=2sinθ

To calculate tanψ, use the formula,

tanψ=rdrdθ=2(1−cosθ)2sinθ=(1−cosθ)sinθ

Substitute θ=π, the value of ψ

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Use your graphing calculator to find the solutions to the equations you solved in the following problems by gra...

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Rate of Change In Exercises 6366, you are given the dollar value of a product in 2012 and the rate at which the...

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Given: BADCDA ABCD Prove: AEDE HINT: Prove BADCDA first.

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In Exercises 2340, determine graphically the solution set for each system of inequality and indicate whether th...

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