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Polar Equation Graphs - PowerPoint PPT Presentation

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Polar Equation Graphs

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  1. Polar Equation Graphs

  2. 5 major kinds of Polar Graphs • Circles r = a sin • Lamiconsr = a + b sin • Roses r = a sin (n • Archimedean Spiral r = a ± bθ • Lemniscates r2 = a2 sin 2

  3. Circles • General Form • r = a cosθ • r = a sin θ

  4. Lamicons r = a ± b cosθ or r = a ± b sin θ 3 scenarios a = b cardioids a > b dimpled a < b loopy

  5. Cardioids (Lamicon)a = b • General form r = a ± a cosθ or r = a ± a sin θ Basically a vaguely Heart shaped graph Can be an upside down or sideways heart. Always includes the origin

  6. Lamiconsa > b Does not ever Include the origin

  7. Lamiconsa < b Includes an Inner loop Always includes The origin

  8. Roses r = a cos bθ a determines radius b relates to the petals r = 3 cos 2θ

  9. Archimedian Spiral r = a ± bθ