Graphing Sine and Cosine Keeper 13 Accelerated PreCalculus Properties of Sine and Cosine General Forms of Sine and Cosine Functions Where a b c and d are constants and neither a nor b is ID: 767757
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Graphing Sine and Cosine Keeper 13 Accelerated Pre-Calculus
Properties of Sine and Cosine
General Forms of Sine and Cosine Functions Where a, b, c, and d are constants and neither a nor b is 0.
Expanding and Compressing The constant factor a in each function Expands the graphs vertically if Compresses the graphs vertically if
Amplitudes of Sine and Cosine Functions The amplitude of a sinusoidal function is half the distance between the maximum and minimum values of the function or half the height of the wave.
Reflections If , the graph of the sinusoidal function is reflected in the x-axis.
Periods of Sine and Cosine Functions The period of a sinusoidal function is the distance between any two sets of repeating points on the graph of the function.
Phase Shift of Sine and Cosine Functions The phase shift of a sinusoidal function is the difference between the horizontal position of the function and that of an otherwise similar sinusoidal function.
Vertical Shift The vertical shift of a sinusoidal function moves the graph up and down. If the function moves up units.If the function moves down units.After a vertical shift, a new horizontal axis known as the midline becomes the reference line or equilibrium point about which the graph oscillates.
Examples State the amplitude, period, phase shift, vertical shift, and reflection of each function. Then graph two periods of the function.