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

Problem

y=1/2*sin(5*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=1/2

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

4. Determine the value of B to find the period. Here, B=5

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

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

Final Answer

Amplitude=1/2,Period=(2*π)/5,Phase Shift=0

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