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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Approximating Area Consider the circle

r = 3 sin θ .

(a) Find the area of the circle.

(b) Complete the table for the areas A of the sectors of the circle between θ = 0 and the values of θ in the table.

θ 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A

(c) Use the table in part (b) to approximate the values of θ for which the sector of the circle composes 1 8 , 1 4 , and 1 2 of the total area of the circle.

(d) Use a graphing utility to approximate, to two decimal places, the angles θ for which the sector of the circle composes 1 8 , 1 4 , and 1 2 of the total area of the 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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