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GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ b ≠ 0

GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ b ≠ 0. HOW THE SIZES OF a, b IMPACT THE GENERAL SHAPE OF THE GRAPH r = a ± b cos θ r = a ± b sin θ. CIRCLE r = a + b cos θ , where |a|=0 r = 2 cos θ.

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GRAPHS OF THE POLAR EQUATIONS r = a ± b cos θ r = a ± b sin θ b ≠ 0

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  1. GRAPHS OF THE POLAR EQUATIONSr = a ± b cos θr = a ± b sin θb ≠ 0

  2. HOW THE SIZES OF a, b IMPACT THE GENERAL SHAPE OF THE GRAPHr = a ± b cos θr = a ± b sin θ

  3. CIRCLEr = a + b cos θ, where |a|=0r = 2 cos θ

  4. LIMACON WITH LOOPr = a + b cos θ, where |a|<|b|r = 1 + 2 cos θ

  5. CARDIOIDr = a + b cos θ, where |a|=|b|r = 2 + 2 cos θ

  6. LIMACON WITH DIMPLEr = a + b cos θ, where |b|<|a|<2|b|r = 3 + 2 cos θ

  7. CONVEX LIMACONr = a + b cos θ, where |a|=2|b|r = 4 + 2 cos θ

  8. CONVEX LIMACONr = a + b cos θ, where |a|>2|b|r = 5 + 2 cos θ

  9. HOW THE TRIGONOMETRIC FUNCTION IMPACTS THE ORIENTATION OF THE GRAPHr = a ± b cos θr = a ± b sin θ

  10. r = a + b cos θ, where a > 0, b > 0r = 1 + 2 cosθ

  11. r = a + b sin θ, where a > 0, b > 0r = 1 + 2 sinθ

  12. HOW THE SIGNS OF a, b IMPACT THE DIRECTION OF THE GRAPHr = a ± b cos θr = a ± b sin θ

  13. r = a + b cos θ, where a > 0, b > 0r = 1 + 2 cos θ

  14. r = a + b cos θ, where a > 0, b < 0r = 1 - 2 cos θ

  15. r = a + b cos θ, where a < 0, b > 0r = -1 + 2 cos θ

  16. r = a + b cos θ, where a < 0, b < 0r = -1 - 2 cos θ

  17. HOW WOULD YOU FINDTHE x- AND y-INTERCEPTSOF A POLAR CURVE r = f(θ) ?

  18. FIND THE VALUES OF rFOR θ = 0, π/2, π AND 3π/2BE CAREFUL OFNEGATIVE VALUES OF r(THE INTERCEPTS WILL APPEAR ON THE “OPPOSITE” SIDE OF THE AXIS)

  19. GRAPHS OF THE POLAR EQUATIONSr = a ± b cos θr = a ± b sin θ 1. Determine the shape of the graph by comparing |a| to |b| and 2|b|2. Determine the axis of symmetry from the trigonometric function3. Determine the direction of the “fat” part from the sign of the trigonometric function4. Find and plot the x- and y-intercepts by finding the values of r for θ = 0, π/2, π AND 3π/25. Connect and form the appropriate shapeCircles, cardioids and limacons with loops pass through the pole; dimpled and convex limacons do not

  20. PUTTING IT TOGETHERGUESS THE GRAPHBY DETERMINING THE SHAPE,THE ORIENTATION,THE DIRECTION & THE INTERCEPTSr = -4 - 3 sin θ

  21. r = -4 - 3 sin θ

  22. PUTTING IT TOGETHERGUESS THE GRAPHBY DETERMINING THE SHAPE,THE ORIENTATION,THE DIRECTION & THE INTERCEPTSr = -4 + 4 cos θ

  23. r = -4 + 4 cos θ

  24. GRAPHS OF THE POLAR EQUATIONSr = a cos nθr = a sin nθ

  25. HOW THE VALUE OF n IMPACTS THE GENERAL SHAPE OF THE GRAPH r = a cos nθr = a sin nθ

  26. r = 3 cos θ

  27. r = 3 cos 2θ

  28. r = 3 cos 3θ

  29. r = 3 cos 4θ

  30. r = 3 cos 5θ

  31. r = 3 cos 6θ

  32. PUTTING IT TOGETHERGUESS THE EQUATIONOF A ROSE CURVE WITH[a] 16 petals[b] 15 petals[c] 14 petals

  33. PUTTING IT TOGETHER[a] r = a sin 8θ orr = a sin 8θ[b] r = a sin 15θ orr = a sin 15θ[c] no such rose curve

  34. HOW THE TRIGONOMETRIC FUNCTION IMPACTS THE ORIENTATION OF THE GRAPHr = a cos nθr = a sin nθ

  35. r = 3 cosθ

  36. r = 3 sinθ

  37. r = 3 cos 2θ

  38. r = 3 sin 2θ

  39. r = 3 cos 3θ

  40. r = 3 sin 3θ

  41. r = 3 cos 4θ

  42. r = 3 sin 4θ

  43. r = 3 cos 5θ

  44. r = 3 sin 5θ

  45. r = 3 cos 6θ

  46. r = 3 sin 6θ

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