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

Problem

y=−3*sin(x)

Solution

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

2. Determine the value of A which is the coefficient of the sine function. Here, A=−3

3. Calculate the amplitude using the formula Amplitude=|A|

Amplitude=|−3|=3

4. Determine the value of B which is the coefficient of x Here, B=1

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

Period=(2*π)/1=2*π

6. Determine the value of C which represents the horizontal displacement. Since there is no value subtracted from x inside the sine function, C=0

7. Identify the phase shift, which is equal to C

Phase Shift=0

Final Answer

Amplitude=3,Period=2*π,Phase Shift=0

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