1. Sinusoidal Modeling (Set Calculators to DEGREE mode)

4. Transformations of Sinusoidal Functions
amplitude |A|=(max – min)/2
period p=2/B (in radians) or p=360/B (in degrees)
So, B=2/p (in radians) or B=360/p (in degrees)
vertical shift of k: (max + min)/2
+k , shift k units up
–k , shift k units down
Phase shift of h (scaled to 360 degrees or 2 radians):
–h, shift h units right
+h, shift h units left
h can be in radians or degrees.

5. Annual Temperature Change (MD)
Amplitude (A)
Period (p) B
Vertical Shift (k)
Phase Shift (h), for Sine
h= –120, since shift RIGHT
Annual Temperature Change (MD)
Sine Model
Phase Shift (b), for Cosine
Cosine Model
b= –210, since shift RIGHT

7. Annual Temperature Change (MO)
Amplitude (A)
Period (p) B
Vertical Shift (k)
Phase Shift (h), for Sine
h= –120, since shift RIGHT
Annual Temperature Change (MO)
Sine Model
Phase Shift (h), for Cosine
Cosine Model
h= –210, since shift RIGHT

8. Sine Model Tide Height Cosine Model Amplitude (A) Period (p) B
Vertical Shift (k)
Phase Shift (h), for Sine
h= +30, since shift LEFT
Sine Model
Tide Height
Phase Shift (h), for Cosine
Cosine Model
h= –60, since shift RIGHT

9. Sine Model Predator/Prey Cosine Model Amplitude (A) Period (p) B
Vertical Shift (k)
Phase Shift (h), for Sine
Sine Model
Predator/Prey
Phase Shift (h), for Cosine
Cosine Model
h= –90, since shift RIGHT