   Chapter 10.5, Problem 11E

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

To determine

To calculate: The value of the area of the section of a polar equation r=sin8θ.

Explanation

Given:

The polar equation is r=sin8θ.

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=sin8θ.

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

Press the enter button and the graph of the function is obtained as follows,

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

0=sin8θ8θ=nπθ=nπ8

Where, n belongs to integer.

From the above graph, it can be seen that all petals are similar. So, consider the one 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=(0)π8=0

For n=1 the value of θ is,

θ=(1)π8=π8

Therefore, the region of θ for which traced the graph of one petal is 0θπ8

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 914, evaluate the expression. 10. 5654

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 1-6, find the absolute maxima and minima for on the interval .

Mathematical Applications for the Management, Life, and Social Sciences 