Find Amplitude, Period, and Phase Shift f(x)=-4sin(pi/7x-pi)-2

Problem

ƒ(x)=−4*sin(π/7*x−π)−2

Solution

1. Identify the standard form of the trigonometric function ƒ(x)=a*sin(b*x−c)+d

2. Determine the constants from the given equation: a=−4 b=π/7 c=π and d=−2

3. Calculate the amplitude using the formula |a|

|−4|=4

4. Calculate the period using the formula (2*π)/b

(2*π)/π/7=2*π⋅7/π=14

5. Calculate the phase shift using the formula c/b

π/π/7=π⋅7/π=7

Final Answer

Amplitude=4,Period=14,Phase Shift=7

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