Module 27  Polar Functions  
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest  
Lesson 27.2: Polar Graphs  
Curves described using polar coordinates can be very interesting and the equations are often much simpler in polar form than they are in rectangular form. This lesson explores graphing polar equations. When graphing polar functions on the TI83,
Graphing in Polar Mode
Graph the polar functions r = 3 sin(2 ).
These window values will be abbreviated as [0, 2 , /24] x [6, 6, 1] x [4, 4, 1]. The values will range from 0 to 2 in steps of /24 and the display window will be determined by the x and yvalues.
This graph is called a fourleafed rose. 27.2.1 Predict the shape of the graph of r = 3sin(3 ) then verify your prediction by displaying the graph on your TI83. Click here for the answer. Finding the Number of Leaves There is a relationship between the value of n in the polar function r = 3sin(n ) and the number of leaves. 27.2.2 Determine how n relates to the number of leaves in the graph of r = 3sin(n ) by graphing the following polar functions. You will need to adjust to 2 for the functions where n is even and to when n is odd. You may also want to make smaller for the last few functions in order to make the graphs smooth.
r = 3sin(4
) Click here for the answer. 27.2.3 How many leaves would you expect in the graph of ? Let and graph the function to verify your prediction. Click here for the answer. Graphing a Cardioid
The graph is called a cardioid because it is heart shaped. It is one of several interesting shapes that are common polar functions. Finding the Slope of a Tangent Line The Derivative feature in the CALC menu, dy/dx, can be used to find the slope of the line tangent to the cardioid
The slope of the tangent line to the cardioid at is approximately 0.414.
Cardioids and Limaçons The equation r = a + bcos represents several families of polar curves depending on the relative values of a and b. 27.2.4 Experiment with this equation using a = b, a > b and a < b. How do the relative values of a and b affect the graph? Click here for the answer. 

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