   Chapter 10.4, Problem 74E

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 = − sin 5 θ

To determine

To graph:

Sketch a graph of the polar equation and then find the tangent line at the pole Explanation

Given: The polar equation is r=sin5θ

Graph is given below:

The given polar equation is r=sin5θ

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

Now consider

r=f(θ)=sin5θ

Differentiate with respect to

θ,

f'(θ)=5cos5θ

Now f(θ)=0

sin5θ=0

θ=0,π5,2π5

Thus, <

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