Problem 59
Question
Use a graphing utility to graph the polar equation. $$r=4 \sin 5 \theta$$
Step-by-Step Solution
Verified Answer
The graph of \(r=4 \sin 5 \theta\) is a rose curve with 5 petals, each extending 4 units from the origin.
1Step 1: Understand the Polar Equation
The equation given is \(r=4 \sin 5 \theta\), which is a rose curve in polar coordinates. The number 5 in sin function indicates that there will be 5 petals in the rose curve as it is an odd number. The coefficient 4 determines the length of the petals.
2Step 2: Set Up the Graphing Utility
You'll need to set up the graphing utility to sketch polar graphs. This step often involves switching the graphing mode from rectangular to polar. In the polar graphing mode, enter the equation \(r=4 \sin 5 \theta\).
3Step 3: Plot the Polar Equation
Plot the graph using your graphing utility. For \(\theta\) values ranging from 0 to 2\(\pi\), the graph should plot the rose curve. The result should be a rose curve with 5 petals, each with a length of 4 units.
4Step 4: Analyze the Graph
Examine the graph of \(r=4 \sin 5 \theta\), and make sure it aligns with the properties of a rose curve. That is, there should be 5 petals, and each should stretch out 4 units from the origin.
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