Find Amplitude, Period, and Phase Shift f(x)=4sin(x)

Problem

ƒ(x)=4*sin(x)

Solution

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

2. Determine the value of a which represents the coefficient of the sine function. Here, a=4

3. Calculate the amplitude using the formula |a|

|4|=4

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

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

(2*π)/|1|=2*π

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

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

0/1=0

Final Answer

Amplitude: *4, Period: *2*π, Phase Shift: *0

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