Find Amplitude, Period, and Phase Shift y=cos(x+1)

Problem

y=cos(x+1)

Solution

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

2. Determine the amplitude by finding the absolute value of the coefficient A in front of the cosine function.

|A|=|1|=1

3. Determine the period using the formula P=(2*π)/|B| where B is the coefficient of x

B=1

P=(2*π)/1=2*π

4. Determine the phase shift by solving the expression inside the cosine for x The phase shift is C in the form (x−C)

x+1=0

x=−1

Final Answer

Amplitude=1,Period=2*π,Phase Shift=−1

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