Find Amplitude, Period, and Phase Shift y=-5sin(1/2x)

Problem

y=−5*sin(1/2*x)

Solution

1. Identify the standard form of the trigonometric function, which is y=A*sin(B*(x−C))+D

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

|A|=|−5|

|A|=5

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

P=(2*π)/(1/2)

P=4*π

4. Determine the phase shift by identifying the horizontal displacement C Since there is no value subtracted from x inside the sine function, C=0

Phase Shift=0

Final Answer

Amplitude=5,Period=4*π,Phase Shift=0

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