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Sketch the graph for a Three Leaf Rose
Solution:
The given equation above is also another type of Polar Equation where the parameters are r and θ. The purpose of converting the equations of Rectangular Coordinate to Polar Coordinate is to simplify the equation. Most of the equations of Polar Equations are complicated if they are written in Rectangular Coordinate. The graphs of Polar Equations are mostly leaves, flowers, and spiral shapes. Let's consider the above equation again
We need to assign the values of θ from 30° to 360° in order to get the values of r as well. All angles must be expressed in radians because radians are unitless values. You can use calculator in order to get the values of r as follows
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| Photo by Math Principles in Everyday Life |
Next, you need a polar paper in order to plot the graph. If you don't have a polar paper, you can use an ordinary graphing paper but you need a compass, protractor, and ruler. As you noticed at the above table that some values of r are negative. We will not use the parameters that have negative values of r. If you plot the values of r and θ and then connect all the points, the graph of the given equation will be like this
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| Photo by Math Principles in Everyday Life |