   Chapter 10.4, Problem 77E

Chapter
Section
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=4cos3θ

Step4: Now press the (GRAPH) key.

The given polar equation is r=4cos3θ

The curve generates when θ changes from [0,π]

Now consider

r=f(θ)=4cos3θ

Differentiate with respect to

θ,

f'(θ)=12sin3θ

Now f(θ)=0

4cos3θ=0

3θ=(2n+1)π2 for nz

θ

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