Find Amplitude, Period, and Phase Shift y=2/3*cos(x/2-pi/4)

Problem

y=2/3*cos(x/2−π/4)

Solution

1. Identify the standard form of the cosine function y=A*cos(B*x−C)+D where A=2/3 B=1/2 and C=π/4

2. Calculate the amplitude by taking the absolute value of the coefficient A

|A|=|2/3|=2/3

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

P=(2*π)/(1/2)=4*π

4. Calculate the phase shift using the formula C/B which determines the horizontal displacement.

Phase Shift=(π/4)/(1/2)=π/2

Final Answer

Amplitude=2/3,Period=4*π,Phase Shift=π/2

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