Find Amplitude, Period, and Phase Shift y=sin(x)+8

Problem

y=sin(x)+8

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 value of C Since there is no horizontal shift inside the sine function, C=0

5. Note that the constant D=8 represents a vertical shift, which does not affect amplitude, period, or phase shift.

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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