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

Problem

y=cos(−6*x)

Solution

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

2. Apply the even function property of cosine, cos(−θ)=cos(θ) to rewrite the expression as y=cos(6*x)

3. Determine the parameters from the equation y=1*cos(6*(x−0))+0 where A=1 B=6 C=0 and D=0

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

Amplitude=|1|=1

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

Period=(2*π)/6=π/3

6. Identify the phase shift using the value of C

Phase Shift=0

Final Answer

Amplitude: *1, Period: π/3, Phase Shift: *0

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