Find Amplitude, Period, and Phase Shift y=4cos(x/2)-5

Problem

y=4*cos(x/2)−5

Solution

1. Identify the standard form of the trigonometric function, which is y=A*cos(B*(x−C))+D

2. Determine the amplitude by taking the absolute value of the coefficient A

|A|=|4|

|A|=4

3. Determine the period using the formula P=(2*π)/B where B is the coefficient of x

B=1/2

P=(2*π)/1/2

P=4*π

4. Determine the phase shift by finding the value of C that shifts the graph horizontally.

C=0

Final Answer

Amplitude=4,Period=4*π,Phase Shift=0

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