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

Problem

y=2*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, B affects the period, C is the phase shift, and D is the vertical shift.

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

|A|=|2|=2

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

Period=(2*π)/2=π

4. Find the phase shift by identifying the value of C Since there is no horizontal shift added or subtracted within the sine function argument, C=0

Phase Shift=0

Final Answer

Amplitude=2,Period=π,Phase Shift=0

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