Find Amplitude, Period, and Phase Shift y=3sin(4x)

Problem

y=3*sin(4*x)

Solution

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

2. Determine the values of the constants from the given equation y=3*sin(4*x)

3. Extract the value for A where A=3

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

5. Extract the value for B where B=4

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

7. Identify the horizontal shift C Since there is no value subtracted from x inside the function, C=0

8. Determine the phase shift, which is equal to C

Final Answer

Amplitude=3,Period=π/2,Phase Shift=0

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