Find Amplitude, Period, and Phase Shift f(x)=5cos(x)+1

Problem

ƒ(x)=5*cos(x)+1

Solution

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

2. Determine the value of A to find the amplitude. Here, A=5 The amplitude is |A|

3. Determine the value of B to find the period. In this function, B=1 The formula for the period is (2*π)/|B|

4. Determine the value of C to find the phase shift. Since there is no horizontal shift inside the cosine function, C=0

5. Calculate the final values based on the identified constants.

Final Answer

Amplitude=5,Period=2*π,Phase Shift=0

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