   Chapter 10, Problem 86RE

Chapter
Section
Textbook Problem

# Tangent Lines at the Pole In Exercises 85 and 86, sketch a graph of the polar equation and find the tangent lines at the pole. r = 3 cos 4 θ

To determine

To graph: The polar equation r=3tanθ and also determine the tangents at the pole.

Explanation

Given:

The polar equation is r=3tanθ.

Calculation:

Consider the provided polar equation: r=3tanθ.

Use Ti83 calculator to graph polar equation. The following steps are needed.

Step 1. Press on button.

Step 2. Press MODE button and choose ‘funct” and in funct choose Pol.

Step 3. prees Y= button and write r1=3tanθ

Step 4. Press GRAPH button.

And the graph of the polar equation r=3tanθ is obtained as below:

Given r=3tanθ

And,

drdθ=ddθ(3tanθ)=3sec2θ

At θ=π6

r=3tan(π6)=4sinπ=0

And

drdθ=12cos3(π3)=12cosπ=12

So, f(π3)=0 and f(π3)0.

If f(α)=0 and f(α)0, then the line θ=α is tangent at the pole to the graph of r=f(θ)

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