Find Amplitude, Period, and Phase Shift y=cos(x/80)

Problem

y=cos(x/80)

Solution

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

2. Determine the values of the constants from the given equation y=cos(1/80*x) where A=1 B=1/80 C=0 and D=0

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

Amplitude=|1|=1

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

Period=(2*π)/(1/80)=160*π

5. Determine the phase shift using the value of C

Phase Shift=0

Final Answer

Amplitude: *1, Period: *160*π, Phase Shift: *0

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