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7.4 Polar Coordinates and Graphs Day 1

7.4 Polar Coordinates and Graphs Day 1. Do Now Evaluate. 7.1 – 7.3 Quiz Review. Retakes by?. Rectangular coordinates. All graphing we’ve done so far has been done with rectangular coordinates ( x,y ) This is not the only way to describe graphs. Polar Coordinates.

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7.4 Polar Coordinates and Graphs Day 1

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  1. 7.4 Polar Coordinates and GraphsDay 1 Do Now Evaluate

  2. 7.1 – 7.3 Quiz Review • Retakes by?

  3. Rectangular coordinates • All graphing we’ve done so far has been done with rectangular coordinates (x,y) • This is not the only way to describe graphs

  4. Polar Coordinates • A point can be described in polar coordinates • The origin is called the pole • The positive half of the x-axis is called the polar axis • The point can be plotted given an angle from the polar axis and a distance R from the pole to the point

  5. Graphing Polar Coordinates • 1) Locate the directed angle • 2) Move a directed distance R from the pole • If R > 0, move along the polar axis • If R < 0, move in the opposite direction • 3) Drawing circles with radius R will help graph each point

  6. Ex • Graph each of the following points • A) • B) • C) • D) • E) • F)

  7. Convert to Polar Coordinates • To convert from rectangular coordinates (x,y) to polar coordinates we create a right triangle that relates rectangular and polar:

  8. Ex • Convert each of the following to polar coordinates • 1) • 2)

  9. Converting to Rectangular Coordinates • Using the same relationship, we can convert to rectangular coordinates:

  10. Ex • Convert each to rectangular coordinates • 1) • 2)

  11. Closure • Convert (-4, 4) to polar coordinates • HW: p.644 #1-37 odds

  12. 7.4 Polar EquationsDay 2 • Do Now • Graph the polar coordinates • 1) • 2) • 3) • 4)

  13. HW Review: p.644 #1-37

  14. Polar and Rectangular Equations • Some curves have simpler equations in polar coordinates than in rectangular coordinates, and vice versa • It can be useful to convert equations so they are easier to work with

  15. Ex • Convert each of the following to a polar equation • 1) • 2)

  16. Ex • Convert each of the following to a rectangular equation • 1) • 2) • 3)

  17. You try • Convert to polar equations • 1) • 2) • Convert to rectangular equations • 3) • 4)

  18. Closure • Convert to a rectangular equation • HW: p.644 #39-61 odds

  19. 7.4 Graphing Polar EquationsDay 3 • Do Now • Convert to a polar equation

  20. HW Review p.644 #39-61

  21. Graphing Polar Equations • To graph polar equations, we want to make a table of values • Pick angles to plug into the function • You should make at least one full revolution of angles to plug in

  22. Ex • Graph

  23. Ex • Graph the polar equation r = 3

  24. Ex • Graph

  25. Ex • Graph

  26. Technology • For more complicated polar functions, use a graphing calculator • The MODE must be set to polar (POL) • Once in polar coordinates, the “X” key can be used to type THETA • Note: you may have to change your windows

  27. Closure • Graph • HW: p.644 #63-97 odds (try not to use calculator for 63-69)

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