Find Amplitude, Period, and Phase Shift f(x)=-3sin(4x-pi)+2

Problem

ƒ(x)=−3*sin(4*x−π)+2

Solution

1. Identify the standard form of the trigonometric function, which is ƒ(x)=a*sin(b*(x−h))+k or ƒ(x)=a*sin(b*x−c)+d

2. Determine 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| where b is the coefficient of x

b=4

P=(2*π)/4

Period=π/2

4. Find the phase shift by setting the argument of the sine function to zero and solving for x or using the formula c/b

4*x−π=0

4*x=π

Phase Shift=π/4

Final Answer

Amplitude=3,Period=π/2,Phase Shift=π/4

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