Find Amplitude, Period, and Phase Shift y=sin(3theta)

Problem

y=sin(3*θ)

Solution

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

2. Determine the value of A by looking at the coefficient of the sine function. Here, A=1

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

4. Determine the value of B by looking at the coefficient of θ Here, B=3

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

6. Determine the phase shift C Since there is no horizontal shift added or subtracted within the sine argument, C=0

Final Answer

Amplitude=1,Period=(2*π)/3,Phase Shift=0

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