1. 2.7 Sinusoidal Graphs; Curve Fitting
Date: ____________

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

3. Period y = sinx 1 period 1 period Period= 2 pattern starts3 2 1 -1 -2 -3
y = sinx
pattern starts
pattern starts
pattern starts
1 period
1 period
Period= 2

4. Period y = cosx 1 period 1 period Period = 2 pattern starts3 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. Period 1 period Period = pattern starts pattern starts 3 2 3 2 1 -1-2 -3
pattern starts
pattern starts
1 period 3 2
Period =

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

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. Sinusoidal Graphs
General Form of Equations
Amplitude =
Period =

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

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

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

21. Sinusoidal Graphs a =3 “sin” 2 Period = b = Amplitude = 3 y = 3sinx 31 -1 -2 -3
y = 3sinx

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

23. Sinusoidal Graphs a = -2 b = “cos” Period = 3 Amplitude = 21 -1 -2 -3
Amplitude = 2
Reflected over x-axis!

24. Sinusoidal Graphs b = a = -3 “cos” Period = 6 Amplitude = 32 1 -1 -2 -3
Reflected over x-axis!

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

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

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

28. Graphing Sinusoidal Functions3 2 1 -1 -2 -3

29. Graphing Sinusoidal Functions3 2 1 -1 -2 -3

30. Graphing Sinusoidal Functions3 2 1 -1 -2 -3

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

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

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

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

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