Find Amplitude, Period, and Phase Shift y=5cos(x+pi/4)

Problem

y=5*cos(x+π/4)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where |A| is the amplitude, (2*π)/B is the period, and C is the phase shift.

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

A=5

Amplitude=|5|=5

3. Calculate the period using the coefficient of x which is B=1

Period=(2*π)/1=2*π

4. Find the phase shift by solving for x in the argument x+π/4=0

x=−π/4

Phase Shift=−π/4

Final Answer

Amplitude=5,Period=2*π,Phase Shift=−π/4

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