Chapter 10.5, Problem 78E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

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=3sinÎ¸

Formula Used:

A=12âˆ«Î±Î²[f(Î¸)]2dÎ¸

Calculation:

To find the limits for Î¸ put r=0

Then 0=3sinÎ¸

â‡’sinÎ¸=sinÏ€

â‡’Î¸=Ï€

So, the area of region lies between the lines Î¸=0 to Î¸=Ï€

Therefore, the area of region is given by:

A=12âˆ«0Ï€[3sinÎ¸]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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