Find Amplitude, Period, and Phase Shift y=-5sin(3x)

Problem

y=−5*sin(3*x)

Solution

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

2. Determine the value of A from the given equation y=−5*sin(3*x)

A=−5

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

Amplitude=|−5|=5

4. Determine the value of B from the coefficient of x

B=3

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

Period=(2*π)/3

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

Phase Shift=0

Final Answer

Amplitude=5,Period=(2*π)/3,Phase Shift=0

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