   Chapter 10.5, Problem 78E

Chapter
Section
Textbook Problem

# Area Find the area of the circle given byr = sin θ + cos θ .Cheek your result by converting the polar equation to rectangular form, then using the formula for the area of a circle.

(a)

To determine

To Calculate: The Area of circle of equation r=3sinθ

Explanation

Given:

The equation of circle: r=3sinθ

Formula Used:

A=12αβ[f(θ)]2dθ

Calculation:

To find the limits for θ put r=0

Then 0=3sinθ

sinθ=sinπ

θ=π

So, the area of region lies between the lines θ=0 to θ=π

Therefore, the area of region is given by:

A=120π[3sinθ]2

(b)

To determine

To Calculate: To complete the tables for areas A of sectors of circle between θ=0 and values of θ in the table

(c)

To determine

Which of the sector of circle composes 18,14 and 12 of total area of circle of equation r=3sinθ by using the table in part (b)

(d)

To determine

Which of the sector of circle composes 18,14 and 12 of total area of circle of equation r=3sinθ by using the table in part (b)

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