Find the amplitude, period, and phase shift of the function. $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$

A) Amplitude 1/2, Period $4 \pi$, phase shift $\pi / 3$

B) Amplitude 1/2, Period $2 \pi$, phase shift $\pi / 3$

C) Amplitude 2, Period $\pi$, phase shift $\pi / 6$

D) Amplitude 2, Period $4 \pi$, phase shift $\pi / 6$

E) Amplitude 2, Period $4 \pi$, phase shift $\pi / 3$

Question

Find the amplitude, period, and phase shift of the function. $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$

A) Amplitude 1/2, Period $4 \pi$, phase shift $\pi / 3$

B) Amplitude 1/2, Period $2 \pi$, phase shift $\pi / 3$

C) Amplitude 2, Period $\pi$, phase shift $\pi / 6$

D) Amplitude 2, Period $4 \pi$, phase shift $\pi / 6$

E) Amplitude 2, Period $4 \pi$, phase shift $\pi / 3$

Quizplus · Accepted Answer

The amplitude is the coefficient of the cosine function, which is 2. The period is calculated as $ \frac{2\pi}{\frac{1}{2}} = 4\pi $. The phase shift is found by solving $ \frac{1}{2}x - \frac{\pi}{6} = 0 $, giving a phase shift of $\frac{\pi}{3}$.

Find the Amplitude, Period, and Phase Shift of the Function y=2cos⁡(12x−π6)y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)y=2cos(21​x−6π​)

Find the Amplitude, Period, and Phase Shift of the Function $y = 2 \cos \left( \frac { 1 } { 2 } x - \frac { \pi } { 6 } \right)$