Mathematical Investigations IV
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Mathematical Investigations IV
Polar Coordinates-Out and Around
Basic Curves – Intro
In previous MI courses, you explored basic types of functions and how changes in the parameters a, b,
h, and k effected the graph of an arbitrary Cartesian function y = a f(bx + h) + k. Now we are going to
explore some basic types of polar graphs along with how these parameters affect the graph of a
function in polar coordinates, r = a f(b + ) + k.
A:
Circles: r = A cos  and r = A sin 
Graph and label carefully the curve r = A cos() for several different values of A. Label each
graph. Be sure to consider the effects on the graph when cosine is replace by sine and also consider
negative values of A.
State the patterns that you find.
Polar 3M.1
Rev. F08
Mathematical Investigations IV
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Remember y = ƒ(x + C)? Now consider r = 4 sin( – ). Try several values of  as you wish.
Sketch and label at least two graphs. What is the effect of ?
B.
Rose Leaves: r = A cos (n) and r = A sin (n)
(We'll consider integer values of n.)
This is another category of basic polar curves. Sketch a few curves and label them carefully.
Do more examples as necessary to complete the summary on the following page.
Equation:
Equation:
Equation:
Equation:
Polar 3M.2
Rev. F08
Mathematical Investigations IV
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Summarize the patterns you've found for rose leaves.
C.
Limaçons: r = A + B cos  and r = A + B sin 
There are three basic types of limaçons, those with |A| = |B|, |A| > |B|, and |A| < |B|. Sketch
several graphs of teach type below and on the next page. State the patterns you find.
Equation:
Equation:
Equation:
Polar 3M.3
Rev. F08
Mathematical Investigations IV
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Equation:
Equation:
Equation:
State the patterns that you've found for limaçons below. Draw more graphs below as needed to help
summarize your ideas.
Polar 3M.4
Rev. F08