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

Problem

y=−3*cos(3*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where |A| is the amplitude, (2*π)/B is the period, and C is the phase shift.

2. Determine the value of A from the given equation y=−3*cos(3*x) Here, A=−3

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

Amplitude=|−3|=3

4. Identify the value of B from the coefficient of x Here, B=3

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

Period=(2*π)/3

6. Identify the phase shift C Since there is no horizontal shift added or subtracted inside the cosine function, C=0

Phase Shift=0

Final Answer

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

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