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

Problem

y=sin(4*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 value of A by looking at the coefficient of the sine function.

A=1

3. Calculate the amplitude using the absolute value of A

Amplitude=|1|=1

4. Identify the value of B from the coefficient of x inside the function.

B=4

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

Period=(2*π)/4=π/2

6. Determine the phase shift C by observing if there is a horizontal translation added to or subtracted from x

C=0

Final Answer

Amplitude=1,Period=π/2,Phase Shift=0

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