# What is the phase shift, vertical displacement with respect to y=sinx for the graph y=3sin(1/2)(x-pi/4)-10?

Jun 17, 2018

Phase Shift $= - \frac{C}{B} = - \frac{\pi}{4} , \frac{\pi}{4}$ to the left.

Vertical Shift $= D = - 10$

#### Explanation:

$y = 3 \sin \left(\frac{1}{2}\right) \left(x - \frac{\pi}{4}\right) - 10$

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

$A = 3 , B = \left(\frac{1}{2}\right) , C = \frac{\pi}{8} , D = - 10$

Amplitude $= | A | = 3$

Period $= \frac{2 \pi}{|} B | = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

Phase Shift $= - \frac{C}{B} = \frac{- \frac{\pi}{8}}{\frac{1}{2}} = - \frac{\pi}{4} , \frac{\pi}{4}$ to the left.

Vertical Shift $= D = - 10$

graph{3 sin(x/2 - pi/8) - 10 [-10, 10, -5, 5]}