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Chapter 6: Problem 68

Use a graphing utility to graph the polar equation. $$r=\frac{3}{\sin \theta}$$

Short Answer

Expert verified
The polar equation \( r = \frac{3}{\sin \theta} \) when graphed using a range of 0 to \( 2\pi \) for \( \theta \) and a graphing utility will produce a limacon with a pole at the origin.

Step by step solution

01

Note the type of the equation

Recognize that the given equation \( r = \frac{3}{\sin \theta} \) is the equation of a limacon with a pole at the origin.
02

Set range for the variable

Decide on an appropriate range for \( \theta \). Here, setting \( \theta \) from 0 to \( 2\pi \) will give a complete graph.
03

Input Polar Equation in Graphing Utility

Enter the polar equation into the graphing utility. Set the mode to 'polar' if necessary. Most graphing utilities offer a polar mode where polar equations can be easily input.
04

Plot the polar equation

Plot the polar equation. You should see a graph that resembles the shape of a limacon, a dimple-shaped graph. This shape is the result of the equation \( r = \frac{3}{\sin \theta} \), which describes a limacon shape.

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