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

Problem

y=2*sin(1/2*x)

Solution

1. Identify the standard form of the trigonometric function y=A*sin(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|=|2|

|A|=2

3. Calculate the period using the formula P=(2*π)/|B| where B=1/2

P=(2*π)/(1/2)

P=4*π

4. Find the phase shift by identifying the value of C Since there is no horizontal translation inside the sine function, C=0

C=0

Final Answer

Amplitude=2,Period=4*π,Phase Shift=0

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