Find Amplitude, Period, and Phase Shift y=5sin(4X)

Problem

y=5*sin(4*x)

Solution

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

2. Determine the values of the constants from the given equation y=5*sin(4*x) where A=5 B=4 C=0 and D=0

3. Calculate the amplitude by taking the absolute value of A

Amplitude=|A|

Amplitude=|5|=5

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

Period=(2*π)/4

Period=π/2

5. Identify the phase shift, which is the value of C Since there is no horizontal shift inside the sine function, the phase shift is 0

Phase Shift=0

Final Answer

Amplitude=5,Period=π/2,Phase Shift=0

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