Determine the phase shift of the function.
-$$y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)$$
A) $\frac { \pi } { 2 }$ units to the right
B) $\frac { \pi } { 2 }$ units to the left
C) -2 units up
D) $- 2$ units down

Question

Quizplus · Accepted Answer

The phase shift of a trigonometric function $y = a \sin(b(x - c)) + d$ or $y = a \cos(b(x - c)) + d$ is determined by the value of $c$. In this case, the function is $y = -2 \sin \left( x - \frac{\pi}{2} \right)$, where $c = \frac{\pi}{2}$. This indicates a phase shift of $\frac{\pi}{2}$ units to the right, because the function is shifted in the positive direction of the x-axis by $\frac{\pi}{2}$.

Determine the Phase Shift of the Function y=−2sin⁡(x−π2)y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)y=−2sin(x−2π​)

Determine the Phase Shift of the Function $y = - 2 \sin \left( x - \frac { \pi } { 2 } \right)$