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Chapter 6: Problem 64

Use a graphing utility to graph the polar equation. $$r=4+2 \cos \theta$$

Short Answer

Expert verified
To graph the polar equation \(r = 4 + 2\cos 胃\), you need to understand polar coordinates, use a graphing utility that supports them, and plot the graph. The resultant plot should resemble a looped shape due to the cosine function in the equation.

Step by step solution

01

Understand Polar Coordinates

Polar coordinates are a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The polar coordinates (r, 胃) are related to the cartesian coordinates (x, y) by the formulas \(x = r \cos 胃\) and \(y = r \sin 胃\). In this problem, we have \(r = 4 + 2\cos 胃\). Our goal is to plot this equation on a graph.
02

Set up the Graphing Utility

Next, you need to use a graphing utility which supports polar coordinate. Obtain access to a tool like this 鈥� for example, many graphic calculators or online tools can achieve this purpose. Enter the function \(r = 4 + 2\cos 胃\) into the utility making sure it's in 'polar mode' to plot polar equations.
03

Plot the Graph

After entering the function, the graphing utility will draw a curve representing the polar equation. It will likely show a looped shape, since the cosine function in the equation results in this type of form.

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