   Chapter 10.5, Problem 12E

Chapter
Section
Textbook Problem

# Finding the Area of a Polar Region In Exercises 5–16, find the area of the region.Interior of r = 1 – sin θ (above the polar axis)

To determine

To calculate: The value of area of the section of the polar equation r=cos5θ.

Explanation

Given:

The Polar equation r=cos5θ.

Formula used:

Area of shaded section bounded by graph of r=f(θ) between the radial lines θ=α and

θ=β is given by:

A=12αβ[f(θ)]2dθ

Calculation:

The provided polar equation is, r=cos5θ.

Draw the graph of the polar equation with the help of Maple graphics whose code is,

Press the enter button and then the graph of the function obtained is,

The value of θ at which the polar equation is equal to zero.

0=cos5θ5θ=(2n+1)π2θ=(2n+1)π10

Where, n belongs to the integers.

From the above graph, it can be seen that all the petals are similar. So, consider the one of the petal of the graph. For one petal of the graph to find the value of θ. For n=0 the value of θ is,

θ=(2(0)+1)π10=π10

For n=1 the value of the θ is,

θ=(2(1)+1)π10=3π10

The section of θ for which drawn the graph of one petal is π10θ3π10

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