Phase Shift Sinusoidal Curve Fitting Phase Shift When

Phase Shift Sinusoidal Curve Fitting

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.

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

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

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.

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

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

On-Line Help �On-line tutorials �On-line examples

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)

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.

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