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

Problem

y=5*cos(4*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=5

3. Calculate the amplitude using the formula Amplitude=|A|

4. Determine the value of B to find the period. Here, B=4

5. Calculate the period using the formula Period=(2*π)/|B|

6. Determine the value of C to find the phase shift. Since there is no horizontal shift inside the function, C=0

Final Answer

Amplitude=5,Period=π/2,Phase Shift=0

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