Find Amplitude, Period, and Phase Shift y=1.5sin(4x)

Problem

y=1.5*sin(4*x)

Solution

1. Identify the standard form of the sine function, which is y=A*sin(B*(x−C))+D where |A| is the amplitude, (2*π)/B is the period, and C is the phase shift.

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

|A|=|1.5|=1.5

3. Calculate the period using the formula Period=(2*π)/B where B=4

(2*π)/4=π/2

4. Find 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=1.5,Period=π/2,Phase Shift=0

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