1. Sinusoidal Curve Fitting
Phase Shift
Sinusoidal Curve Fitting

2. Phase Shift
When the graph is shifted right or left, this is called a phase shift.
For the graphs of
The phase shift is to the left if f < 0 and to the right if f > 0.

3. Phase Shift
Just remember transformations. Inside parentheses moves the graph the given value opposite sign.

4. Examples Find the amplitude, period, and phase shift of
Y = 3 sin (2x – π), and graph the function
Amplitude = 3

5. Graph Start by plotting the phase shift
The end point will be the period + phase shift
Now take the starting and ending point and divide by two or add the phase shift to the points that are plotted on the standard sine curve.

6. Examples Find the amplitude, period, and phase shift of
y = 2 cos (4x + 3π) and graph the function

7. Summary 1. Determine the amplitude and period
2. Determine the starting point of one cycle (phase shift)
3. Determine the ending point of one cycle of the graph (phase shift + period)
4. Divide the interval into four subintervals
5. Use the standard curve to graph the shape
6. Fill in one cycle of the graph

8. On-Line Help
On-line tutorials
On-line examples

9. Finding Sinusoidal Functions from Data
Steps for Fitting Data to a Sine Function
1. Determine A, the amplitude of the function
2. Determine the vertical shift of the function (B)

10. Finding Sinusoidal Functions from Data
3. Determine ω. Since the period T, the time it takes for the data to repeat, is
4. Determine the phase shift of the function by solving the equation for Φ by choosing an ordered pair from the given data. We choose the ordered pair for which y is smallest in order to maintain consistency.

11. Examples
Use Data from p. 441
Example 5 p. 444
P. 447 #21