   Chapter 10.5, Problem 10E

Chapter
Section
Textbook Problem

Finding the Area of a Polar Region In Exercises 7-18, Find the area of the region.Two petals of   r = 4 sin 3 θ

To determine

To calculate: The value of area of two petal of polar equation r=4sin3θ.

Explanation

Given:

The polar equation is r=4sin3θ.

Calculation:

Shaded section of two petal circumscribed by the curve r=4sin3θ is shown below:

Use the following steps in Ti-83 calculator to plot the graph:

Step1: Press MODE Key and select POL mode.

Step2: Press (Y=) Key.

Step3: Press r1=4sin3θ

Step4: Now press the [GRAPH] key and the graph is found:

From the figure, it can be seen that pf polar region lies among 0 to 2π.

The section for polar axis is drawn out for one petal is 0θπ3

Substitute 4sin3θ for r, π3 for β and 0 for α

The area of shaded section bounded by graph of r=f(θ) between the radial lines θ=α and θ=β.

So,

A=12αβ[f(θ]2.dθ

Substitute these values in above formula and get,

A=120π3[4sin3θ]2

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