Find the amplitude, the period in radians, the phase shift in radians,and the vertical shift. y=9sin(4Theta -(pi )/(6))+3 Select one: a. Amplitude: 9 Period: (pi )/(2) Phase shift: Right (pi )/(24) Vert. shift: Up 3 b. Amplitude: 9 Period: (pi )/(2) Phase shift: Left (pi )/(24) Vert. shift: Down 3 c. Amplitude: 9 Period: (pi )/(2) Phase shift: Right (pi )/(54) Vert. shift: Up 3 d. Amplitude: (1)/(7) Period: 2pi Phase shift: Right (7pi )/(6)

The given function is .* **Amplitude:** The amplitude is the absolute value of the coefficient of the sine function. In this case, the amplitude is .* **Period:** The period of a sine function is given by , where is the coefficient of . In this case, , so the period is .* **Phase Shift:** The phase shift is determined by the term inside the sine function. We rewrite the argument of the sine function as . The phase shift is given by the value subtracted from . In this case, it is . Since it is subtracted, the phase shift is to the *right* by .* **Vertical Shift:** The vertical shift is the constant term added to the sine function. In this case, the vertical shift is 3. Since it is positive, the shift is *up* by 3.Therefore, the correct answer is:a. Amplitude: 9Period: Phase shift: Right Vert. shift: Up 3Final Answer: The final answer is