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.
$$y=3+5 \cos \frac{1}{4}\left(\theta-240^{\circ}\right)$$

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Key Concepts

Sinusoidal Axis

The sinusoidal axis, also known as the midline, is the horizontal line that represents the central value around which the sine or cosine function oscillates. It is determined by the vertical shift in the function, indicating how far above or below the standard position the graph is moved.

Phase Displacement

The phase displacement, or phase shift, refers to the horizontal translation of the function. It shows where the cycle of the trigonometric function starts relative to the origin. A positive phase displacement shifts the graph to the right, while a negative one shifts it to the left.

Amplitude

The amplitude is the distance from the midline (or sinusoidal axis) of a trigonometric function to its peak or trough. It measures the vertical stretch or compression of the function and is given by the absolute value of the coefficient multiplying the cosine or sine function.

Period

The period is the length of one complete cycle of the trigonometric function. It indicates how far along the horizontal axis the function repeats itself. In a transformed cosine or sine function, the period is typically calculated by dividing 360° (or 2? radians) by the absolute value of the coefficient affecting the variable inside the trigonometric function.

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