Find Amplitude, Period, and Phase Shift y=5/3*sin(-(2pi)/3x)

Problem

y=5/3*sin(−(2*π)/3*x)

Solution

1. Identify the standard form of the sine function y=A*sin(B*(x−C)) where |A| is the amplitude, the period is (2*π)/|B| and C is the phase shift.

2. Determine the amplitude by taking the absolute value of the coefficient A=5/3

|A|=|5/3|=5/3

3. Calculate the period using the formula P=(2*π)/|B| where B=−(2*π)/3

P=(2*π)/|−(2*π)/3|

P=(2*π)/(2*π)/3

P=3

4. Find the phase shift by identifying the horizontal displacement C Since there is no constant added or subtracted inside the sine argument, C=0

Phase Shift=0

Final Answer

Amplitude=5/3,Period=3,Phase Shift=0

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