Find Amplitude, Period, and Phase Shift y=2sin(5x)

Problem

y=2*sin(5*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=2

3. Calculate the amplitude using the absolute value of A

Amplitude=|2|=2

4. Determine the value of B to find the period. Here, B=5

5. Calculate the period using the formula P=(2*π)/B

Period=(2*π)/5

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

Phase Shift=0

Final Answer

Amplitude=2,Period=(2*π)/5,Phase Shift=0

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