Find Amplitude, Period, and Phase Shift y=-5cos(3x)

Problem

y=−5*cos(3*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 which is the coefficient of the cosine function. Here, A=−5

3. Calculate the amplitude by taking the absolute value of A

Amplitude=|−5|=5

4. Determine the value of B which is the coefficient of x Here, B=3

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

Period=(2*π)/3

6. Determine the phase shift C by looking for a horizontal translation inside the argument. Since there is no constant added to or subtracted from 3*x C=0

Phase Shift=0

Final Answer

Amplitude=5,Period=(2*π)/3,Phase Shift=0

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