Find Amplitude, Period, and Phase Shift f(t)=-2/3*sin(6t)

Problem

ƒ(t)=−2/3*sin(6*t)

Solution

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

2. Determine the value of A from the given function ƒ(t)=−2/3*sin(6*t)

A=−2/3

3. Calculate the amplitude by taking the absolute value of A

Amplitude=|−2/3|=2/3

4. Identify the value of B from the coefficient of t inside the sine function.

B=6

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

Period=(2*π)/6=π/3

6. Determine the phase shift C by observing if there is a horizontal shift added to or subtracted from t Since 6*t is not written as 6(t - C),t*h*e*v*a*l*u*e*o*ƒ$ is zero.

Phase Shift=0

Final Answer

Amplitude=2/3,Period=π/3,Phase Shift=0

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