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Chapter 7: Problem 65

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

Short Answer

Expert verified
The graph of the polar equation \(r = 4 + 2 \sin \theta\) represents a circle with the center at r=4 and radius of 2, offset by a sinusoidal variation due to the dependent \(\theta\) variable. The graph can best be obtained using a graphing utility which allows input of polar equations.

Step by step solution

01

Understand the Polar Equation

Analyze the equation \(r = 4 + 2 \sin \theta\), and understand that it's a circle centered at r=4 with radius 2. The variation of \(\theta\) causes points to move around the circle.
02

Convert to Cartesian coordinates

If needed for understanding, the equation can temporarily be converted to cartesian coordinates using the transformation \(x = r \cos \theta\) and \(y = r \sin \theta\). Substituting \(r\) will then give a cartesians equation in x and y.
03

Graph the Equation

Use a graphing tool to plot the equation. Start with \(\theta = 0\) and gradually increase the angle while calculating the corresponding r. The points thus obtained can be plot on the polar grid.
04

Interpret the Graph

Verify the graph. For \(\theta = 0\) and \(\theta = \pi\), the radius r should be at maximal and minimal distance from origin respectively.

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Most popular questions from this chapter

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