Find Amplitude, Period, and Phase Shift y=-4cos(6x)

Problem

y=−4*cos(6*x)

Solution

1. Identify the standard form of the trigonometric function, which is y=A*cos(B*(x−C))+D In this equation, A=−4 B=6 C=0 and D=0

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

Amplitude=|A|

Amplitude=|−4|=4

3. Calculate the period using the formula P=(2*π)/|B|

Period=(2*π)/6

Period=π/3

4. Identify the phase shift by looking at the horizontal displacement C Since there is no value subtracted from or added to x inside the function, the shift is zero.

Phase Shift=0

Final Answer

Amplitude=4,Period=π/3,Phase Shift=0

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