Find Amplitude, Period, and Phase Shift y=3cos(x+1)

Problem

y=3*cos(x+1)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

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

|A|=|3|

|A|=3

3. Calculate the period using the formula P=(2*π)/|B| In this equation, B=1

P=(2*π)/1

P=2*π

4. Find the phase shift by solving the expression inside the cosine for zero, x+1=0 or identifying C from the form B*(x−C)

x+1=0

x=−1

Final Answer

Amplitude=3,Period=2*π,Phase Shift=−1

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