   Chapter 10.5, Problem 62E

Chapter
Section
Textbook Problem

# Finding the Arc Length of a Polar Curve In Exercises 59-64, use a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve. r = 2 sin ( 2 cos θ ) ,       [ 0 , π ]

To determine

To graph: The polar equation r=2sin(2cosθ) over the interval [0,π] by the use of graphing utility and to determine the approximate length of the curve by using integration capability of graphing utility.

Explanation

Given:

The polar equation r=2sin(2cosθ) over the interval [0,π].

Formula used:

Arc length of polar curve is s=αβr2+(drdθ)2dθ.

Graph:

Use the following steps in TI-83 for the curve of polar equation:

Step 1:

Open TI-83 calculator.

Step 2:

Press MODE and select the Pol option.

Step 3:

Press Y=.

Step 4:

Enter r1=2sin(2cosθ).

Step 5:

Press WINDOW to access window editor.

Step 6: Set window as

θmin=0,θmax=π,θstep=0.1308996,Xmin=3,Xmax=3,Xscl=1,Ymin=3,Ymax=3,Yscl=1.

Step 7: Press TRACE.

The curve obtained is:

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