Find Amplitude, Period, and Phase Shift y=4sin(2x)

Problem

y=4*sin(2*x)

Solution

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

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

|A|=|4|

A=4

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

Period=(2*π)/2

Period=π

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=4,Period=π,Phase Shift=0

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