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Chapter 6: Problem 34

Use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{12}{2-\cos \theta}\)

Short Answer

Expert verified
To identify the graph, you will input the equation \(r=\frac{12}{2-\cos \theta}\) into a graphing utility with the settings set to polar mode. The graph analyzed is the Limacon curve - a type of polar curve. The exact identification may depend on the graphing utility used.

Step by step solution

01

Understand the given equation

The polar equation we have is \(r=\frac{12}{2-\cos \theta}\). This doesn't immediately form a shape we can identify, so we'll need to utilize a graphing utility to draw out the curve and identify it.
02

Input the equation into the graphing utility

Next, input the equation \(r=\frac{12}{2-\cos \theta}\) into the graphing utility. Ensure to set the graph to polar mode because we're dealing with a polar equation and the parameters in terms of \(r\) and \(\theta\).
03

Analyze the graph

Once the graphing utility plots the points corresponding to the polar equation, analyze the resulting graph. Look out for recognizable patterns or shapes. Depending on the utility used, it might even provide you with the type of graph plotted.

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