   Chapter 10.4, Problem 72E

Chapter
Section
Textbook Problem

# Tangent Lines at the Pole In Exercises 69–76, sketch a graph of the polar equation and find the tangents at the pole.r = 3(1 – cos θ )

To determine

To graph: The polar equation, r=3(1cosθ) also compute the tangent at the pole for the equation.

Explanation

Given:

The polar equation is r=3(1cosθ).

Graph:

Consider the equations,

r=3(1cosθ) …… (1)

Construct the table for the values of r and θ after that plot them on graph.

For θ=0, substitute 0 for θ in equation (1);

r=3(1cos(0))=3(11)=3(0)=0

For θ=π3, substitute π3 for θ in equation (1);

r=3(1cos(π3))=3(112)=32

For θ=π2, substitute π2 for θ in equation (1);

r=3(1cos(π2))=3(10)=3

For θ=2π3, substitute 2π3 for θ in equation (1);

r=3(1cos(2π3))=3(1(12))=3(32)=92

For θ=π, substitute π for θ in equation (1);

r=3(1cos(π))=3(1(1))=3(2)=6

Construct the table, using various values of θ and r, for the function r=3(1cosθ).

 θ 0 π3 π2 2π3 π r 0 32 3 92 6

Plot the above points on the graph.

For θ lies in the interval [0,π3],

For θ lies in the interval [0,π2],

For θ lies in the interval [0,2π3],

For θ lies in the interval [0,π],

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