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r = 3 sin 20

r = 3 sin 20

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Graph the Polar Equation Below** \( r = 3 \sin 2\theta \) --- In this example, we are given a polar equation to graph. The equation is in polar form where \( r \) represents the radius or the distance from the origin, and \( \theta \) represents the angle in radians. The equation \( r = 3 \sin 2\theta \) is a polar equation that describes a rose curve, which typically has a distinctive shape with petals. Because the equation includes \( 2\theta \), this particular rose curve will have symmetry and multiple petals. To graph this equation: 1. Calculate \( r \) for various values of \( \theta \). 2. Plot the corresponding points on the polar coordinate system. 3. Connect these points smoothly to visualize the shape of the curve. Given the form of the function \( 3 \sin 2\theta \), you can expect the curve to have 4 petals (since the coefficient of \( \theta \) is 2, the number of petals is doubled). Here is a step-by-step method to plot the graph: 1. Choose values of \( \theta \) such as 0, \( \pi/8 \), \( \pi/4 \), \( 3\pi/8 \), and \( \pi/2 \). 2. Calculate \( r \) for each value of \( \theta \). 3. Use the polar coordinates to plot points on the graph. 4. Join the points smoothly to form the complete rose curve. Feel free to use a graphing tool or calculator to assist in plotting more precise points for an accurate graph.
Transcribed Image Text:**Graph the Polar Equation Below** \( r = 3 \sin 2\theta \) --- In this example, we are given a polar equation to graph. The equation is in polar form where \( r \) represents the radius or the distance from the origin, and \( \theta \) represents the angle in radians. The equation \( r = 3 \sin 2\theta \) is a polar equation that describes a rose curve, which typically has a distinctive shape with petals. Because the equation includes \( 2\theta \), this particular rose curve will have symmetry and multiple petals. To graph this equation: 1. Calculate \( r \) for various values of \( \theta \). 2. Plot the corresponding points on the polar coordinate system. 3. Connect these points smoothly to visualize the shape of the curve. Given the form of the function \( 3 \sin 2\theta \), you can expect the curve to have 4 petals (since the coefficient of \( \theta \) is 2, the number of petals is doubled). Here is a step-by-step method to plot the graph: 1. Choose values of \( \theta \) such as 0, \( \pi/8 \), \( \pi/4 \), \( 3\pi/8 \), and \( \pi/2 \). 2. Calculate \( r \) for each value of \( \theta \). 3. Use the polar coordinates to plot points on the graph. 4. Join the points smoothly to form the complete rose curve. Feel free to use a graphing tool or calculator to assist in plotting more precise points for an accurate graph.
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