Find Amplitude, Period, and Phase Shift y=-3sin(-6x+pi/2)

Problem

y=−3*sin(−6*x+π/2)

Solution

1. Identify the standard form of the trigonometric function, which is y=A*sin(B*(x−h))+k or y=A*sin(B*x−C)+k In this equation, A=−3 B=−6 and C=−π/2

2. Calculate the amplitude by taking the absolute value of the coefficient A

|A|=|−3|

Amplitude=3

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

P=(2*π)/|−6|

P=(2*π)/6

Period=π/3

4. Calculate the phase shift by setting the argument of the sine function to zero and solving for x or using the formula C/B from the form B*x−C

−6*x+π/2=0

−6*x=−π/2

x=(−π/2)/(−6)

Phase Shift=π/12

Final Answer

Amplitude=3,Period=π/3,Phase Shift=π/12

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