# Feb 11, 2011 - PowerPoint PPT Presentation

Feb 11, 2011

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Feb 11, 2011

## 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 5 7 4 1

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

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

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

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

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

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

10. 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:

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

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

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

14. 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

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

16. 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

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

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

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

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

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

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

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

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

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

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

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

28. 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:

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

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

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

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

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

34. 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.

35. 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. ?

36. 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.

37. 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.

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

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

40. 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:

41. 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:

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

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