Find Amplitude, Period, and Phase Shift y=sin(x)+2

Problem

y=sin(x)+2

Solution

1. Identify the standard form of the trigonometric function, which is y=A*sin(B*(x−C))+D

2. Determine the amplitude by looking at the coefficient A in front of the sine function. Since A=1 the amplitude is |A|=1

3. Calculate the period using the formula P=(2*π)/|B| Here, the coefficient of x is B=1 so P=(2*π)/1=2*π

4. Find the phase shift by identifying the value of C inside the argument of the sine function. Since there is no horizontal shift added to or subtracted from x C=0

5. Note that the +2 represents a vertical shift D=2 which does not affect the amplitude, period, or phase shift.

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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