Chapter 10.4, Problem 107E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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(1âˆ’cosÎ¸) at Î¸=Ï€.

Formula used:

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

tanÏˆ=rdrdÎ¸

Calculation:

Consider the polar equation, r=2(1âˆ’cosÎ¸)

Differentiate r with respect to Î¸,

drdÎ¸=ddÎ¸(2(1âˆ’cosÎ¸))=ddÎ¸(2âˆ’2cosÎ¸)=2sinÎ¸

To calculate tanÏˆ, use the formula,

tanÏˆ=rdrdÎ¸=2(1âˆ’cosÎ¸)2sinÎ¸=(1âˆ’cosÎ¸)sinÎ¸

Substitute Î¸=Ï€, the value of Ïˆ

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