Find Amplitude, Period, and Phase Shift y=2sin(-4x)

Problem

y=2*sin(−4*x)

Solution

1. Identify the standard form of the trigonometric function y=A*sin(B*(x−C)) where |A| is the amplitude, (2*π)/|B| is the period, and C is the phase shift.

2. Determine the coefficients from the given equation y=2*sin(−4*x) which are A=2 B=−4 and C=0

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

|A|=|2|=2

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

P=(2*π)/|−4|=(2*π)/4=π/2

5. Identify the phase shift C by observing that there is no horizontal displacement added to or subtracted from the x term.

C=0

Final Answer

Amplitude=2,Period=π/2,Phase Shift=0

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