Find the specified quantity.
-Find the phase shift of $y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)$
A) $- \frac { \pi } { 6 }$
B) $- \frac { \pi } { 2 }$
C) $\frac { \pi } { 6 }$
D) $\frac { \pi } { 4 }$

Question

Quizplus · Accepted Answer

The phase shift of a sine function in the form $y = a \sin(bx + c) + d$ is given by $-\frac{c}{b}$. For the given function $y = 4 - 2 \sin \left( 3x + \frac{\pi}{2} \right)$, $b = 3$ and $c = \frac{\pi}{2}$, so the phase shift is $-\frac{\pi/2}{3} = -\frac{\pi}{6}$.

Find the Specified Quantity y=4−2sin⁡(3x+π2)y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)y=4−2sin(3x+2π​)

Find the Specified Quantity $y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)$