Find Amplitude, Period, and Phase Shift y=cos(x)-4

Problem

y=cos(x)−4

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.

A=1

Amplitude=|1|=1

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

B=1

Period=(2*π)/1=2*π

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

C=0

Phase Shift=0

5. Note that the constant −4 represents a vertical shift D which does not affect the amplitude, period, or phase shift.

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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