Chapter 10.4, Problem 77E

### 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

# Tangent Lines at the Pole In Exercises 73-80, sketch a graph of the polar equation and find the tangent line(s) at the pole (if any). r = 4 cos 3 θ

To determine

To Graph:

The polar equation r=4cos3θ and then find the tangent line at the pole.

Explanation

Graph:

Graph is given below:

The Ti-83 calculator steps are as follows:

Step1: Press MODE Key and select POL mode.

Step2: Press (Y=) Key.

Step3: Type the equation r1=4cos3Î¸

Step4: Now press the (GRAPH) key.

The given polar equation is r=4cos3Î¸

The curve generates when Î¸ changes from [0,Ï€]

Now consider

r=f(Î¸)=4cos3Î¸

Differentiate with respect to

Î¸,

f'(Î¸)=âˆ’12sin3Î¸

Now f(Î¸)=0

â‡’4cos3Î¸=0

â‡’3Î¸=(2n+1)Ï€2 for nâˆˆz

â‡’Î¸

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