Find Amplitude, Period, and Phase Shift y=sin(6x)

Problem

y=sin(6*x)

Solution

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

2. Determine the value of A to find the amplitude. In the given equation y=sin(6*x) the coefficient A is 1

3. Calculate the amplitude using the formula Amplitude=|A|

Amplitude=|1|=1

4. Identify the value of B to find the period. In this equation, B=6

5. Calculate the period using the formula Period=(2*π)/|B|

Period=(2*π)/6=π/3

6. Identify the horizontal shift C to find the phase shift. Since there is no value subtracted from or added to x inside the sine function, C=0

Phase Shift=0

Final Answer

Amplitude=1,Period=π/3,Phase Shift=0

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