# How do you translate the graph of y=sin(x-pi/6)+1?

Oct 13, 2016

Translate the wave y = sin x by moving it in x+ direction, through $\frac{\pi}{6}$ units, and get graph of $y = \sin \left(x - \frac{\pi}{6}\right)$. Now, move this in y+ direction, through 1 unit, for $y = \sin \left(x - \frac{\pi}{6}\right) + 1$.

#### Explanation:

$y = \sin \left(x - \frac{\pi}{6}\right) + 1$ is a sine wave, with period $2 p$, , amplitude 1

unit, mean (level ) axis y =1 ( vertical phase shift 1) and horizontal

phase shift $\frac{\pi}{6}$ units.,

Translate the wave y = sin x by moving it in x+ direction, through

$\frac{\pi}{6}$ units, and get graph of $y = \sin \left(x - \frac{\pi}{6}\right)$. Now, move this in y+

direction, through 1 unit, for $y = \sin \left(x - \frac{\pi}{6}\right) + 1$.