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2.7 Sinusoidal Graphs; Curve Fitting

2.7 Sinusoidal Graphs; Curve Fitting. Date: ____________. Sinusoidal Graphs. Graphs of sine and cosine functions. Periodic Function. Functions whose graphs have a repeating pattern. Sinusoidal Graphs. Period. The horizontal length of each cycle in a periodic graph. 3 2 1 -1

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2.7 Sinusoidal Graphs; Curve Fitting

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  1. 2.7Sinusoidal Graphs; Curve Fitting Date: ____________

  2. Sinusoidal Graphs Graphs of sine and cosine functions. Periodic Function Functions whose graphs have a repeating pattern. Sinusoidal Graphs Period The horizontal length of each cycle in a periodic graph.

  3. 3 2 1 -1 -2 -3 Period y = sinx pattern starts pattern starts pattern starts 1 period 1 period Period= 2

  4. Period y = cosx 3 2 1 -1 -2 -3 pattern starts pattern starts pattern starts 1 period 1 period Period = 2

  5. Period 3 2 1 -1 -2 -3 pattern starts pattern starts 1 period Period= 

  6. 3 2 Period 3 2 1 -1 -2 -3 pattern starts pattern starts 1 period Period =

  7. Amplitude Amplitude Half the distance between the maximum and minimum of a sinusoidal graph.

  8. Amplitude 3 2 1 -1 -2 -3 max. Amplitude min. Amplitude = 1

  9. Amplitude max. 3 2 1 -1 -2 -3 Amplitude Amplitude = 2 min.

  10. Amplitude max. 3 2 1 -1 -2 -3 Amplitude min. Amplitude = 1

  11. Amplitude Amplitude = 2 3 2 1 -1 -2 -3 max. 3 Amplitude min.

  12. Amplitude = Period = Sinusoidal Graphs General Form of Equations

  13. Sinusoidal Graphs y = -4cos5x y = 3sin4x Amplitude = Amplitude = Period = Period =

  14. Writing Equations Answer these questions first: • Is it a “sin” or “cos” graph? • What is the amplitude? • What is the period? • Is the graph reflected? • Is it shifted up/down? • Is it shifted left/right?

  15. Writing Equations b = a = 4 Write an equation: cosine graph amplitude = 4 Period =  b = = 2

  16. Writing Equations b = a = 3 Write an equation: sine graph amplitude = 3 Period = 4 b =

  17. Writing Equations b = Write an equation: sine graph amplitude = 2 Period = 3 Reflected over x-axis a = -2 b =

  18. Write an equation: cosine graph amplitude = ½ Period = Reflected over x-axis Writing Equations b = Invert and multiply! a = b =

  19. Writing Equations Write an Equation Sine graph Amplitude = 5 Period = Shifted up 2 a = b =

  20. Sinusoidal Graphs “sin” a =1 b =  Period = 3 2 1 -1 -2 -3 Amplitude = 1 y = sin2x

  21. Sinusoidal Graphs “sin” 2 Period = a =3 b = Amplitude = 3 3 2 1 -1 -2 -3 y = 3sinx

  22. Sinusoidal Graphs “cos” a =1 Period = b = 1 3 2 1 -1 -2 -3 Amplitude =

  23. Sinusoidal Graphs “cos” -2 a = b = Period = 3 3 2 1 -1 -2 -3 Amplitude = 2 Reflected over x-axis!

  24. Sinusoidal Graphs “cos” b = Period = 6 a = -3 Amplitude = 3 3 2 1 -1 -2 -3 Reflected over x-axis!

  25. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3 y = 3sin4x

  26. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3 y = 2sinx

  27. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3 y = -3sin2x

  28. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3

  29. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3

  30. Graphing Sinusoidal Functions 3 2 1 -1 -2 -3

  31. Phase Shift • Horizontal translations of sine and cosine graphs. Right Left Phase Shift Phase Shift

  32. right Phase Shift Amp = 3 T = P.S. =

  33. left Phase Shift Amp = 2 T = P.S. =

  34. Phase Shift “Cosine” Amplitude = 5 Period =  Phase shift =

  35. Phase Shift “sine” Amplitude = 3 Period = 4 Phase shift =

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