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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.

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Feb 11, 2011


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    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.