Find Amplitude, Period, and Phase Shift y=1/2sin(x+pi/2)

Problem

y=1/2*sin(x+π/2)

Solution

1. Identify the standard form of the trigonometric function, which is y=A*sin(B*(x−C))+D In this equation, A=1/2 B=1 C=−π/2 and D=0

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

Amplitude=|A|

Amplitude=|1/2|=1/2

3. Calculate the period using the formula P=(2*π)/|B|

Period=(2*π)/1

Period=2*π

4. Find the phase shift by identifying the value of C from the horizontal displacement (x−C) Since the expression is (x+π/2) we rewrite it as (x−(−π/2))

Phase Shift=−π/2

Final Answer

Amplitude=1/2

Period=2*π

Phase Shift=−π/2

Want more problems? Check here!