Find the specified quantity.
-Find the phase shift of $y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)$.
A) $- \frac { \pi } { 3 }$
B) $\frac { \pi } { 15 }$
C) $- \frac { \pi } { 15 }$
D) $\frac { \pi } { 6 }$

Question

Quizplus · Accepted Answer

The phase shift of a trigonometric function of the form $y = a \sin(bx - c) + d$ or $y = a \cos(bx - c) + d$ is given by $\frac{c}{b}$. In this case, $c = \frac{\pi}{3}$ and $b = 5$, so the phase shift is $\frac{\frac{\pi}{3}}{5} = \frac{\pi}{15}$.

Find the Specified Quantity y=2−2sin⁡(5x−π3)y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)y=2−2sin(5x−3π​)

Find the Specified Quantity $y = 2 - 2 \sin \left( 5 x - \frac { \pi } { 3 } \right)$