Find Amplitude, Period, and Phase Shift y=1/4sin(x+pi/4)

Problem

y=1/4*sin(x+π/4)

Solution

1. Identify the standard form of the sine function y=A*sin(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|=|1/4|=1/4

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

Period=(2*π)/1=2*π

4. Find the phase shift by identifying C from the expression (x+π/4) Since the standard form uses (x−C) we rewrite the expression as (x−(−π/4))

C=−π/4

Final Answer

Amplitude: 1/4, Period: *2*π, Phase Shift: −π/4

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