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Intro to Polar Coordinates

Intro to Polar Coordinates. Warm Up: If I were to turn 3 π /4 degrees from the positive x-axis and then walk out 4 units from the origin in that direction, find the coordinates of the point I would be standing on.

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Intro to Polar Coordinates

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  1. Intro to Polar Coordinates Warm Up: If I were to turn 3π/4 degrees from the positive x-axis and then walk out 4 units from the origin in that direction, find the coordinates of the point I would be standing on. Objectives: Be able to graph and convert between rectangular and polar coordinates. Be able to convert between rectangular and polar equations. TS: Examine Information from more than one point of view.

  2. Polar Coordinate System A point in the Polar coordinate system is (r, θ), where r is the directed distance from the pole and θ is the directed angle from the polar axis

  3. Graphing Polar Coordinates A (1, π/4) B (3, - π/3) C (3, 5π/3) D (-2, -7π/6) E (-1, 5π/4)

  4. Conversions between rectangular and polar Given (r, θ), the point (x, y) would be in the same location given all the following relations were true. x = rcosθ r2 = x2 + y2 y = rsinθ

  5. Graphing Polar Coordinates (-√2, 3π/4) Convert to Rectangle, Graph both.

  6. Use the conversions to change the given coordinates to their Polar Form (-4, -4) (-1, √3)

  7. Converting/Graphing Equations Polar to Rectangular • r = 2

  8. Converting/Graphing Equations Polar to Rectangular 2)θ = π/3

  9. Converting/Graphing Equations Polar to Rectangular 3) r = secθ

  10. Converting/Graphing Equations Rectangular to Polar 4) x2 + y2 = 16

  11. Converting/Graphing Equations Rectangular to Polar 5) y = x

  12. Converting/Graphing Equations Rectangular to Polar – Convert to polar form. Identify the figure and graph it. Confirm by graphing the polar as well on your calculator 6) x2 + y2 – 8y = 0

  13. More Challenging Conversions 7) Polar to Rectangular

  14. More Challenging Conversions 8) Rectangular to Polar (x – 1)2 + (y + 4)2 = 17

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