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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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Vocabulary

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.  

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

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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.  and 
  2.  and 
  3.  and 
.
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.

Transformations

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  or  called? _________________________

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

  1. How do sine and cosine graphs differ?
.
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