Determine the phase shift of the function.
-$$y = 5 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$$
A) $\pi$ units to the left
B) $\frac { \pi } { 2 }$ units to the left
C) $\frac { \pi } { 4 }$ units to the right
D) $5 \pi$ units to the right

Question

Quizplus · Accepted Answer

The phase shift is $\frac { \pi } { 2 }$ units to the left. This is because the argument of the cosine function is $\frac { 1 } { 2 } x + \frac { \pi } { 2 }$, which means that the graph of the function is shifted $\frac { \pi } { 2 }$ units to the left compared to the graph of the function $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$.

Determine the Phase Shift of the Function y=5cos⁡(12x+π2)y = 5 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)y=5cos(21​x+2π​)

Determine the Phase Shift of the Function $y = 5 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 2 } \right)$