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

Problem

y=cos(−2*x)

Solution

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

2. Apply the even property of the cosine function, cos(−θ)=cos(θ) to rewrite the expression as y=cos(2*x)

3. Determine the amplitude by finding the absolute value of the coefficient A Here, A=1

|A|=|1|=1

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

P=(2*π)/2=π

5. Find the phase shift by identifying the horizontal displacement C Since there is no value added to or subtracted from x inside the function, C=0

Phase Shift=0

Final Answer

Amplitude=1,Period=π,Phase Shift=0

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