Module 25  Polar Functions  
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest  
Lesson 25.2: 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 TI89, is the independent variable and r is the dependent variable. Angles are positive if measured in the counterclockwise direction from the positive xaxis. The independent variable in Polar Graph mode is .
Graphing in Polar Mode Change to Polar graphing mode on your TI89.
Graph the polar function r = 3 sin(2 ).
is the green feature above .
This graph is called a fourleafed rose. 25.2.1 Predict the shape of the graph of r = 3sin(3 ) then verify your prediction by displaying the graph on your TI89. Click here to check your 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. 25.2.2 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. 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. 25.2.3 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 Graph the cardioid r = 2(1 + cos ) using the following viewing window. Finding a Tangent Line Use the Tangent feature to find the equation of the line tangent to the cardioid at
The equation of the tangent line at is approximately y = 0.414x + 3.414, which is given in xycoordinates and shown at the bottom of the screen. Finding Arc Length Find the arc length of the cardioid r = 2(1 + cos ) for .
The arc length over the interval is 16 units. 

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