Find Amplitude, Period, and Phase Shift f(x)=3sin(x)

Problem

ƒ(x)=3*sin(x)

Solution

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

2. Determine the value of a which is the coefficient of the sine function. Here, a=3

3. Calculate the amplitude using the formula |a|

|3|=3

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 h which represents the horizontal shift. Since there is no value subtracted from or added to x inside the sine function, h=0

7. Identify the phase shift as the value of h

h=0

Final Answer

Amplitude=3,Period=2*π,Phase Shift=0

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