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Polar Coordinates

Polar Coordinates. a different system of plotting points and coordinates than rectangular (x , y) it is based on the ordered pair (r , θ), where r is the distance from the origin and θ is the angle in standard position

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Polar Coordinates

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

  2. Example: Plot the point (3 , 150º) 3 Some other ways of naming that same point: (3 , -210º),

  3. What about negative values of r? answer: to graph (-3 , 150º), go 3 units out in the opposite direction from 150º 3

  4. Finding all polar coordinates of (r , θ) Positive r: add multiples or 360º or 2π Negative r: add 180º or π, then you can add multiples of 360º or 2π

  5. Coordinate Conversion • Use the following to convert (x , y)  (r , θ) • Use the following to convert (r , θ)  (x , y)

  6. Example #1 Convert to (x , y):

  7. Example #2 Convert into (r , θ): (-3 , -7)

  8. Practice Problems 1.) convert into (x , y): 2.) convert into (r , θ) : (4 , -2)

  9. Practice Problems 1.) convert into (x , y):

  10. 2.) convert into (r , θ) : (4 , -2) Practice Problems

  11. Equation Conversion • equations in polar form have r in terms of θ example : r = 4cosθ • these equations can be graphed using the calculator or by hand (section 6-5) • To convert equations between rectangular form and polar form use:

  12. Example #3 Convert into a rect. equation This is the equation of a circle w/ center at (2 , 0) and radius 2

  13. Example #4 Convert into polar equation this is the equation of a circle with center at (3 , 2) and radius of I’ll do this problem on the board.

  14. Practice Problem #3 Convert into a rectangular equation:

  15. Distance Between Two Polar Coordinates • use Law of Cosines • the two r values are the sides and θ can be found by taking the difference between the two angles • See textbook example #7 for details r1 θ r2

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