Find Amplitude, Period, and Phase Shift y=3sin(2x)

Problem

y=3*sin(2*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=3 The amplitude is |A|

3. Calculate the amplitude using the absolute value.

Amplitude=|3|=3

4. Identify the value of B to find the period. Here, B=2

5. Apply the formula for the period of a sine function, which is (2*π)/|B|

Period=(2*π)/2=π

6. Identify the value of C to find the phase shift. Since there is no horizontal shift inside the function, C=0

Phase Shift=0

Final Answer

Amplitude=3,Period=π,Phase Shift=0

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