Find the amplitude, period, phase displacement, and...

Find the amplitude, period, phase displacement, and sinusoidal axis location Without using your grapher, sketch the graph by locating critical points. Then check your graph using your grapher.
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Key Concepts

Amplitude

Amplitude refers to the distance from the sinusoidal axis (or midline) to either the peak (maximum) or the trough (minimum) of the graph. It determines how 'tall' or 'deep' the waves of the sinusoid appear, and it is calculated as the absolute value of the coefficient in front of the cosine or sine function.

Period

The period of a sinusoid is the horizontal length over which the function completes one full cycle before repeating. It is determined by the coefficient inside the function that multiplies the variable, typically given by the formula Period = (full cycle length) / (frequency coefficient), indicating how the function is stretched or compressed along the horizontal axis.

Phase Shift

Phase shift is the horizontal displacement of the sinusoidal graph from its standard position. It tells us how far and in which direction the basic cosine or sine graph has been shifted along the horizontal axis. This shift is determined by the horizontal translation term within the argument of the cosine or sine function.

Vertical Shift (Sinusoidal Axis)

The vertical shift, or sinusoidal axis, is the constant term added to the function, which moves the midline of the sinusoid up or down on the graph. This shift establishes a new central line about which the sinusoidal function oscillates.

Critical Points Identification

Critical points in a sinusoidal graph include the maximum, minimum, and the points where the graph crosses the midline. Identifying these points is essential for sketching the graph accurately, as they define the key features and shape of the sine or cosine curve over one period.

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