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

Problem

y=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 value of A from the coefficient of the sine function, which is 1

3. Calculate the amplitude using the formula Amplitude=|A|

Amplitude=|1|=1

4. Determine the value of B from the coefficient of x which is 1/2

5. Calculate the period using the formula Period=(2*π)/|B|

Period=(2*π)/(1/2)=4*π

6. Determine the phase shift C by observing that there is no horizontal translation added to or subtracted from x inside the function.

Phase Shift=0

Final Answer

Amplitude=1,Period=4*π,Phase Shift=0

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