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

Problem

y=5*sin(2*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=5

3. Calculate the amplitude using the absolute value of A

Amplitude=|5|=5

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

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

Period=(2*π)/2=π

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=5,Period=π,Phase Shift=0

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