Based on material learned earlier in the course. The purpose...

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. For $y=\frac{3}{2} \cos (6 x+3 \pi),$ find the amplitude, period, and phase shift. Then graph the function, showing at least two periods.

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
For $y=\frac{3}{2} \cos (6 x+3 \pi),$ find the amplitude, period, and phase shift. Then graph the function, showing at least two periods.

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Key Concepts

Phase Shift

The phase shift of a trigonometric function indicates the horizontal translation of the graph relative to its standard position. It is found by analyzing the angle added to or subtracted from the variable inside the function, showing how the graph has been shifted left or right.

Graphing Trigonometric Functions

Graphing trigonometric functions involves applying transformations such as amplitude changes, period adjustments, phase shifts, and vertical shifts to the basic trigonometric graphs. This process helps visualize how these functions oscillate and how their key properties determine the shape and position of the graph over the coordinate plane.

Amplitude

The amplitude of a trigonometric function measures its maximum displacement from the function's midline. It is a property that indicates how 'tall' or 'short' the wave is and is determined by the absolute value of the coefficient in front of the trigonometric function.

Period

The period of a trigonometric function represents the length over which the function completes one full cycle and then repeats itself. It is calculated based on the coefficient of the variable inside the function, and it indicates how the function is stretched or compressed horizontally.