   Chapter 10.5, Problem 58E

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 = sec θ ,       [ 0 , π 3 ] .

To determine

To graph: The polar equation r=secθ over the interval [0,π3] by the use of graphing utility. Also, to determine the approximate length of the curve by the use of integration capability of graphing utility.

Explanation

Given:

Polar equation r=secθ over the interval [0,π3].

Formula used:

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

Graph:

For the curve of polar equation use TI-83 as graphing utility and do the following these steps:

Step 1: Open TI-83 calculator.

Step 2: Press MODE and select the Pol option.

Step 3: Press Y=.

Step 4: Enter r1=secθ.

Step 5: Press WINDOW to access window editor.

Step 6: Set window as

θmin=0,θmax=π3,θstep=0.1308996,Xmin=1,Xmax=5,Xscl=1,Ymin=1,Ymax=5,Yscl=1.

Step 7: Press TRACE.

The obtained curve is

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