1. Sinusoidal Modeling (Set Calculators to DEGREE mode)

4. Transformations of Sinusoidal Functions
Amplitude |a|: a controls vertical stretching/shrinking
Period p can be in radians or degrees: p is the horizontal length to complete one cycle
Horizontal shift b can be in radians or degrees: b controls horizontal stretching/shrinking
Vertical shift d:
+d , shift d units up
–d , shift d units down
Horizontal phase shift c (proportionally scaled to 2 radians or 360):
–c, shift c units right
+c, shift c units left
where, xstart corresponds with the first point of the sine or cosine cycle

5. Annual Temperature Change (MD)
Amplitude (a)
Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
c= –120, since shift RIGHT
Annual Temperature Change (MD)
Sine Model
Phase Shift (c), for Cosine
Cosine Model
c= –210, since shift RIGHT

6. Annual Temperature Change (MD)
Amplitude (a)
Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
Annual Temperature Change (MD)

8. Annual Temperature Change (MO)
Amplitude (a)
Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
c= –120, since shift RIGHT
Annual Temperature Change (MO)
Sine Model
Phase Shift (h), for Cosine
Cosine Model
c= –210, since shift RIGHT

9. Annual Temperature Change (MO)
Amplitude (a)
Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
Annual Temperature Change (MO)

10. Sine Model Tide Height Cosine Model Amplitude (a) Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
c= -150, since shift RIGHT
Sine Model
Tide Height
Phase Shift (h), for Cosine
Cosine Model
c= –60, since shift RIGHT

11. Tide Height Amplitude (a) Period (p) b Vertical Shift (d)
Phase Shift (c), for Sine
Tide Height

12. Sine Model Predator/Prey Cosine Model Amplitude (a) Period (p) b
Vertical Shift (d)
Phase Shift (c), for Sine
Sine Model
Predator/Prey
Phase Shift (h), for Cosine
Cosine Model
h= –90, since shift RIGHT

13. Predator/Prey Amplitude (a) Period (p) b Vertical Shift (d)
Phase Shift (c), for Sine
Predator/Prey