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

Question

Quizplus · Accepted Answer

The phase shift of a trigonometric function in the form $y = a \sin(bx - c)$ or $y = a \cos(bx - c)$ is calculated as $\frac{c}{b}$. For the given function $y = 2 \sin \left( 2x - \frac{\pi}{2} \right)$, the phase shift is $\frac{\frac{\pi}{2}}{2} = \frac{\pi}{4}$ units to the right, because the subtraction in the argument $(2x - \frac{\pi}{2})$ indicates a shift to the right.

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

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