Module 27 - Polar Functions | |||||||||||||||||||||||||||||
Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test | |||||||||||||||||||||||||||||
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 TI-83,
Graphing in Polar Mode
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Graph the polar functions r = 3 sin(2
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These window values will be abbreviated as [0, 2
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![]() This graph is called a four-leafed rose.
27.2.1 Predict the shape of the graph of r = 3sin(3
Finding the Number of Leaves
There is a relationship between the value of n in the polar function r = 3sin(n
27.2.2 Determine how n relates to the number of leaves in the graph of r = 3sin(n
r = 3sin(4
Click here for the answer.
27.2.3 How many leaves would you expect in the graph of
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 ![]() ![]()
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The slope of the tangent line to the cardioid at
Cardioids and Limaçons
The equation r = a + bcos
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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