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Transformations of Polar Graphs

Alteration of graph based on changing constants and/or function of a polar equation.

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Polar Coordinates and Graphs

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Complete the chart.
Word Definition
Polar Coordinates ________________________________________________________
______________ a graph of two heart shaped loops reflected across the "x" axis
______________ a graph with a sinusoidal curve looping around the origin
Transformation ________________________________________________________

Polar Coordinates

How many radians are in a circle? _____________

How do you convert from degrees to radians? ____________________________

In your own words, explain how to graph polar points on a graph: _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Name the coordinates of the points on this graph: 

A: ____________

B: ____________

C: ____________

Graph the following on a calculator:

  1.  r=1+3sinθ
  2. r=1+2cosθ
  3. (1.5,2π3)

Give three alternate sets of coordinates for the given point within the range 360θ360 .

  1. (3,120)
  2. (1,240)
  3. (4,345)

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Distance Between Two Polar Coordinates

What is the Law of Cosines? ______________________________________

How do we have to transform the Law of Cosines to make it a distance formula for polar coordinates? _____________________________________________________

Therefore, what is the Polar Distance Formula? ______________________________________


Find the distance between each set of points:

  1. (3,260) and (2,90)
  2. (4,45) and (6,150)
  3. (5,60) and (1,250)
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Give an equation for a line on a polar graph: _______________________________

Give an equation for a circle on a polar graph: _______________________________

Graph the following polar equations on the same polar grid and compare the graphs.



What are the graphs of r=a±bsinθ or r=a±bcosθ called? _________________________

Graph each function using your calculator and sketch on your paper.

  1. r=23cos(θ)
  2. r=1+2sin(θ)
  3. r=2+5cos(θ)
  4. How do sine and cosine graphs differ?
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