Solve the problem.
-For the equation $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.
A) (i) $\frac { 1 } { 2 }$
(ii) $\pi$
(iii) $\pi$

B) (i) $\frac { 1 } { 2 }$
(ii) $\frac { \pi } { 2 }$
(iii) $\pi$

C) (i) 2
(ii) $\pi$
(iii) $\pi$

D) (i) 2
(ii) $2 \pi$
(iii) $2 \pi$

Question

Solve the problem.
-For the equation $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.
A) (i) $\frac { 1 } { 2 }$
(ii) $\pi$
(iii) $\pi$

B) (i) $\frac { 1 } { 2 }$
(ii) $\frac { \pi } { 2 }$
(iii) $\pi$

C) (i) 2
(ii) $\pi$
(iii) $\pi$

D) (i) 2
(ii) $2 \pi$
(iii) $2 \pi$

Quizplus · Accepted Answer

The amplitude is given by the absolute value of the coefficient in front of the cosine function, which is $ \frac { 1 } { 2 } $. The phase shift is determined by solving $2x - 2\pi = 0$, which gives $x = \pi$, indicating a phase shift of $\pi$. The period of a cosine function is given by $ \frac { 2\pi } { B } $, where $B$ is the coefficient of $x$ inside the cosine function. Here, $B = 2$, so the period is $ \frac { 2\pi } { 2 } = \pi$.

Solve the Problem y=−12cos⁡(2x−2πy = - \frac { 1 } { 2 } \cos ( 2 x - 2 \piy=−21​cos(2x−2π

Solve the Problem $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$