1 / 105

Feb 11, 2011

Feb 11, 2011. The transformed trigonometric functions. f(x) = a sin b(x – h) + k. Recall which is which in the rule:. Match the parameters to the number:. k. h. b. a. Match the parameters to the number:. k. h. b. a. 5. 7. 4. 1. Which is affected by parameter a?. a = 1.

camden-marsh
Download Presentation

Feb 11, 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Feb 11, 2011 The transformed trigonometric functions

  2. f(x) = a sin b(x – h) + k • Recall which is which in the rule:

  3. Match the parameters to the number: k h b a

  4. Match the parameters to the number: k h b a 5 7 4 1

  5. Which is affected by parameter a? a = 1 Amplitude Period Frequency l.o.o.

  6. Which is affected by parameter a? a = 2 Amplitude Period Frequency l.o.o.

  7. Which is affected by parameter a? a = 3 Amplitude Period Frequency l.o.o.

  8. Which is affected by parameter a? Amplitude Period Frequency l.o.o.

  9. In fact, parameter a = amplitude Amplitude Period Frequency l.o.o.

  10. y = 2 cos x y = 8 sin 2x y = -3 cos x y = 4 sin 9x - 2 What would be the amplitude:

  11. y = 2 cos x y = 8 sin 2x y = -3 cos x y = 2.4 sin 9x - 2 amplitude = 2 amplitude = 8 amplitude = 3 amplitude = 2.4 What would be the amplitude:

  12. What would be the value of a in the rule?

  13. What would be the value of a in the rule? a = 5

  14. What would be the value of a in the rule?

  15. What would be the value of a in the rule? a = 4

  16. What would be the value of a in the rule? a = 4

  17. Another way to find amplitude: Amplitude = half the distance between the Max and min values = (M – m)  2 = (2 - -6)  2 = 8  2 = 4

  18. Another way to find amplitude: Amplitude = half the distance between the Max and min values = (M – m)  2 = (2 - -6)  2 = 8  2 = 4 2 -6

  19. What would be the value of a in the rule?

  20. What would be the value of a in the rule? a = 1 Amplitude = half the distance between the Max and min values = (M – m)  2 = (2 - 0)  2 = 2  2 = 1

  21. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude =

  22. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude = |a|

  23. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude = |a|

  24. Which is affected by parameter b? b = 1 Amplitude Period Frequency l.o.o.

  25. Which is affected by parameter b? b = 2 Amplitude Period Frequency l.o.o.

  26. Which is affected by parameter b? b = 4 Amplitude Period Frequency l.o.o.

  27. Which is affected by parameter b? Amplitude Period Frequency l.o.o.

  28. Which is affected by parameter b? 4 cycles Amplitude Period Frequency l.o.o.

  29. Which is affected by parameter b? Amplitude Period Frequency l.o.o.

  30. In fact, b = frequency y = sin 4x Amplitude Period Frequency = 4 = b l.o.o.

  31. y = cos 4x y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 What would be the frequency:

  32. y = cos 4x y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 frequency = 4 frequency = 2 frequency =  frequency = 9 What would be the frequency:

  33. What would be the value of b in the rule?

  34. What would be the value of b in the rule? b = 1

  35. What would be the value of b in the rule?

  36. What would be the value of b in the rule? b = 3

  37. What would be the value of b in the rule?

  38. What would be the value of b in the rule? b = 0.5

  39. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency =

  40. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency = |b|

  41. And if 4 cycles have a total width of 2.... ...then one of those cycles must have a width of... y = sin 4x Amplitude Period Frequency l.o.o.

  42. And if 4 cycles have a total width of 2.... ...then one of those cycles must have a width of... y = sin 4x Amplitude Period Frequency l.o.o. ?

  43. And if 4 cycles have a total width of 2.... ...then one of those cycles must have a width of... y = sin 4x Amplitude Period = Frequency l.o.o.

  44. And if 4 cycles have a total width of 2.... ...then one of those cycles must have a width of... y = sin 4x Amplitude Period = Frequency l.o.o.

  45. In fact, period = y = sin 4x Amplitude Period = Frequency l.o.o.

  46. In fact, period = y = sin 4x Amplitude Period = Frequency l.o.o.

  47. y = cos 4x y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 period = period = period = period = What would be the period:

  48. y = cos 4x y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 period = period = period = period = What would be the period:

  49. In general then: • For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency = |b| Period =

  50. Which is affected by parameter h? h = 0 Amplitude Period Frequency l.o.o.

More Related