Find Amplitude, Period, and Phase Shift f(x)=6sin(1/4*(pix)-pi)-3

Problem

ƒ(x)=6*sin(1/4*(π*x)−π)−3

Solution

1. Identify the standard form of the trigonometric function ƒ(x)=A*sin(B*(x−C))+D or ƒ(x)=A*sin(B*x−C)+D In this expression, A=6 B=π/4 C=π and D=−3

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

Amplitude=|A|

Amplitude=|6|=6

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

Period=(2*π)/π/4

Period=2*π⋅4/π=8

4. Find the phase shift by setting the argument of the sine function to zero or using the formula C/B from the form ƒ(x)=A*sin(B*x−C)+D

Phase Shift=π/π/4

Phase Shift=π⋅4/π=4

Final Answer

Amplitude=6,Period=8,Phase Shift=4

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