1. Sinusoidal Modeling I. Getting the trig equation from data points.
Standard formula: y = D + A trig B(x + C).
A) A = Amplitude (the height [y values] of the graph).
1) A = ½ the distance between the highest & lowest pts.
2) A = ½ (maximum y value – minimum y value).
a) If the first time (x) value is a min, then use –A.
B) Period: How quickly the graph repeats. P = 2π/B
1) P is the x distances between …
*a) P = 2•(the x value for max pt – the x value for min pt)
b) P = (the x value for 1st max pt – x value for next max)
c) P = (the x value for 1st min pt – x value for next min)
2) If P = 2π/B , then B = 2π/P

2. Sinusoidal Modeling I. Getting the trig equation from data points.
Standard formula: y = D + A trig B(x + C).
C) Horizontal translation (the C term). A shift along the x-axis.
(It’s best to use the cosine function as your trig function.)
1) Find the 1st time value (is it a max or min?). Influences A.
a) That x value is the C term (change the sign).
b) If (x , y) is the max point, then (C , max y value).
becomes f(x) = cos (x – C) [we change the sign].
D) Vertical translation (the D term). A shift along the y-axis
1) Find the average of the max & min heights.
a) D = ½ (max height + min height) [height is y values]

3. Sinusoidal Modeling Standard formula: y = D + A trig B(x + C).
Example: The table below shows the high temperatures for each month for Tallahassee. Write a trig model for the data.
A = ½ (maximum y value – minimum y value)
A = ½ (92.0 – 63.8)
A = ½ (28.2)
A = 14.1
P = 2 • (the x value for max pt – the x value for min pt)
P = 2 • (7 – 1)
P = 2 • (6) B = 2π/P = 2π/12 = π/6
P = 12 M 1 2 3 4 5 6 7 8 9 10 11 12 T
63.8
67.4
74.0
80.0
86.5
90.9
92.0
91.5
88.5
81.2
72.9
65.8

4. Use cosine: y = 77.9 + 14.1 cos π/6(x – 7)
Sinusoidal Modeling
Standard formula: y = D + A trig B(x + C).
Horizontal translation (the C term). A shift along the x-axis.
Find the x value when its at its maximum height (y). (7, 92.0)
That x value is the C term (change the sign). So C = –7
Vertical translation (the D term). A shift along the y-axis
D = ½ (max height + min height) [height is y values]
D = ½ ( ) = ½ (155.8) =
A = B = π/ C = – D = 77.9
Use cosine: y = cos π/6(x – 7) M 1 2 3 4 5 6 7 8 9 10 11 12 T
63.8
67.4
74.0
80.0
86.5
90.9
92.0
91.5
88.5
81.2
72.9
65.8