Polar Coordinates

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Polar Coordinates

• a different system of plotting points and
  coordinates than rectangular (x , y)
• it is based on the ordered pair (r , ?), where
  r is the distance from the origin and ? is the
  angle in standard position
• unlike for trig. problems r can be positive or
  negative (? can also be either)
• each point can be named with different polar
  coordinates (an infinite number of them)

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• Example Plot the point (3 , 150º)

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Some other ways of naming that same point (3 ,
-210º),
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• What about negative values of r?
• answer to graph (-3 , 150º), go 3 units out in
  the opposite direction from 150º

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4

• Finding all polar coordinates of (r , ?)
• Positive r add multiples or 360º or 2p
• Negative r add 180º or p, then you can add
  multiples of 360º or 2p

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Coordinate Conversion

• Use the following to convert (x , y) ? (r , ?)

• Use the following to convert (r , ?) ? (x , y)

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• Example 1 Convert to (x , y)

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• Example 2 Convert into (r , ?) (-3 , -7)

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• Practice Problems
• 1.) convert into (x , y)

2.) convert into (r , ?) (4 , -2)
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• Practice Problems
• 1.) convert into (x , y)

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• Practice Problems

2.) convert into (r , ?) (4 , -2)
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Equation Conversion

• equations in polar form have r in terms of
  ? example r 4cos?
• these equations can be graphed using the
  calculator or by hand (section 6-5)
• To convert equations between rectangular form and
  polar form use

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• Example 3 Convert into a rect. equation

This is the equation of a circle w/ center at (2
, 0) and radius 2
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• Example 4 Convert into polar equation

this is the equation of a circle with center at
(3 , 2) and radius of
Ill do this problem on the board.
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• Practice Problem 3 Convert into a rectangular
  equation

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Distance Between Two Polar Coordinates

• use Law of Cosines
• the two r values are the sides and ? can be found
  by taking the difference between the two angles
• See textbook example 7 for details

r1
?
r2