Find Amplitude, Period, and Phase Shift y=sin(x)+7

Problem

y=sin(x)+7

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. Here, A=1

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

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

5. Note that the +7 represents a vertical shift D which does not affect the amplitude, period, or phase shift.

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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