   Chapter 10.4, Problem 105E

Chapter
Section
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(1cosθ) 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(1cosθ) 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(1cosθ)

Differentiate r with respect to θ,

drdθ=ddθ(2(1cosθ))=ddθ(22cosθ)=2sinθ

To calculate tanψ, use the formula,

tanψ=rdrdθ=2(1cosθ)2sinθ=(1cosθ)sinθ

Substitute θ=π, the value of ψ

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