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Polar Coordinates

Polar Coordinates. Plotting Points Using Polar Coordinates Determining Different Representations of a Point Converting a Point from Polar Coordinates to Rectangular Coordinates Converting a Point from Rectangular Coordinates to Polar Coordinates

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Polar Coordinates

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  1. Polar Coordinates • Plotting Points Using Polar Coordinates • Determining Different Representations of a Point • Converting a Point from Polar Coordinates to Rectangular Coordinates • Converting a Point from Rectangular Coordinates to Polar Coordinates • Converting an Equation from Rectangular Form to Polar Form • Converting an Equation from Polar Form to Rectangular Form Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ melikyan@nccu.edu

  2. Plotting Points Using Polar Coordinates Plot the following points in a polar coordinate system. a. b. c. A B

  3. Determining Different Representations of the Same Point The point is shown. Determine a different representation of point P that have the specified conditions.

  4. Determining Different Representations of the Same Point The point is shown. r > 0; negative angle; coterminal with given angle

  5. Determining Different Representations of the Same Point The point is shown. r < 0; positive angle; coterminal with given angle

  6. Relationships Used when Converting a Point from Polar Coordinates to Rectangular Coordinates

  7. Converting a Point from Polar Coordinates to Rectangular Coordinates Determine the rectangular coordinates for the given polar coordinates.

  8. Converting a Point from Polar Coordinates to Rectangular Coordinates Determine the rectangular coordinates for the given polar coordinates.

  9. Converting Rectangular Coordinates to Polar Coordinates for Points Lying Along an Axis Determine the polar coordinates for the given rectangular coordinates. The point lies along the negative x-axis. So The distance from the origin to the point is 4.5 units, so r = 4.5.

  10. Converting a Point from Rectangular Coordinates to Polar Coordinates Determine the polar coordinates for the given rectangular coordinates. Find the value of r. The point (2, 2) lies in Quadrant IV.

  11. Converting a Point from Rectangular Coordinates to Polar Coordinates-cont Determine the point. Find the value of Use inverse tangent.

  12. Converting an Equation from Rectangular Form to Polar Form Convert the equation given in rectangular form into polar form. Replace x with r cos .

  13. Converting an Equation from Rectangular Form to Polar Form Convert the equation given in rectangular form into polar form. Replace x with r cos  and y with r sin 

  14. Converting an Equation from Polar Form to Rectangular Form Convert the equation given in rectangular form into polar form. Replace r cos  with x and r sin  with y

  15. Converting an Equation from Polar Form to Rectangular Form Convert the equation given in rectangular form into polar form. First multiply both sides of the equation by r.

  16. Graphs in Polar coordinates • Sketching Equations of the Form • Sketching Equations of the Form • Sketching Equations of the Form • Sketching Equations of the Form • Sketching Equations of the Form

  17. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation The graph is a line passingthrough the pole that makes an angle of 2/3 with the polar axis.

  18. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation

  19. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation The graph is a horizontal line equivalent to the equation y = 3.

  20. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation Convert the equation to rectangular form.

  21. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation The graph is a circle centered at the pole with radius of length |3| = 3.

  22. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation Convert the equation to rectangular form. Complete the square. The equation is a circle with center located 2 units directly above the pole with a radius of 2 units.

  23. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation Make a table of values.

  24. Sketching the Graph of a Polar Equation-cont Sketch the graph of the polar equation

  25. Sketching the Graph of a Polar Equation-cont Sketch the graph of the polar equation

  26. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation The graph is symmetric; complete the graph by drawing the reflection.

  27. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation

  28. Sketching the Graph of a Polar Equation Sketch the graph of the polar equation The equation is a lemniscate. The length of each loop is 3 units.

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