Find the phase shift of the function.
-$$y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)$$
A) $4 \pi$ units down
B) $4 \pi$ units up
C) $\frac { \pi } { 8 }$ units to the right
D) $\frac { \pi } { 2 }$ units to the left

Question

Quizplus · Accepted Answer

The phase shift of a trigonometric function of the form $y = a \sin(bx - c)$ or $y = a \cos(bx - c)$ is given by $\frac{c}{b}$ units to the right (if $c > 0$) or to the left (if $c < 0$). For the given function $y = -4 \sin(4x - \frac{\pi}{2})$, $b = 4$ and $c = \frac{\pi}{2}$, so the phase shift is $\frac{\frac{\pi}{2}}{4} = \frac{\pi}{8}$ units to the right.

Find the Phase Shift of the Function y=−4sin⁡(4x−π2)y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)y=−4sin(4x−2π​)

Find the Phase Shift of the Function $y = - 4 \sin \left( 4 x - \frac { \pi } { 2 } \right)$