Find Amplitude, Period, and Phase Shift y=cos(x)+3

Problem

y=cos(x)+3

Solution

1. Identify the standard form of the trigonometric 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.

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

4. Find the phase shift by identifying the value of C inside the argument of the cosine function.

5. Observe that the constant D=3 represents a vertical shift, which does not affect amplitude, period, or phase shift.

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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