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Transformations of Polar Graphs

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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: _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Name the coordinates of the points on this graph: 

A: ____________

B: ____________

C: ____________

Graph the following on a calculator:

  1.  r = 1 + 3 sin \theta
  2. r = 1 + 2 cos \theta
  3. \left(1.5, \frac{2\pi}{3}\right)

Give three alternate sets of coordinates for the given point within the range -360^\circ \leq\theta\leq 360^\circ .

  1. (3, 120^\circ )
  2. (1, 240^\circ )
  3. (4, 345^\circ )

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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? ______________________________________

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Find the distance between each set of points:

  1. (-3, 260^\circ ) and (2, 90^\circ )
  2. (4, -45^\circ ) and (6, 150^\circ )
  3. (-5, -60^\circ ) and (1, 250^\circ )
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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.

r & = 5 + 5 \sin \theta && r = 5 - 5 \sin \theta \\r & = 5(1 + \sin \theta) && r = 5(1 - \sin \theta)

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What are the graphs of r = a \pm b \sin \theta or r = a \pm b \cos \theta called? _________________________

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

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