# What is the phase shift, vertical displacement with respect to y=sinx for the graph y=-3sin(6x+30^circ)-3?

May 10, 2018

As below.

#### Explanation:

Standard form of sine function is $y = A \sin \left(B x - C\right) + D$

Given equation is $y = - 3 \sin \left(6 x + {30}^{\circ}\right) - 3$

$y = - 3 \sin \left(6 x + \left(\frac{\pi}{6}\right)\right) - 3$

$A = - 3 , B = 6 , C = - \frac{\pi}{6} , D = - 3$

$A m p l i t u \mathrm{de} = | A | = 3$

$\text{Period } = P = \frac{2 \pi}{|} B | = \frac{2 \pi}{6} = \frac{\pi}{3}$

$\text{Phase Shift " = -C / B = -(pi/6) / 6 = pi/36, " to the right}$

$\text{Vertical Shift = D = -3, " 3 down}$

$\text{For y = sin x fumction}$,

$\text{Phase Shift " = 0, "Vertical Shift } = 0$

#:. Phase Shift w.r.t. " y = sin x " is " pi/3 to the right.

$\text{Vertical displacement w.r.t. " y = sin x " is " -3 " or 3 units down}$

graph{-3sin(6x+ 30) - 3 [-10, 10, -5, 5]}