# How do you graph  y=sin(x-135)?

Jul 13, 2018

As below.

#### Explanation:

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

$y = \sin \left(x - {135}^{\circ}\right) = \sin \left(x - \frac{3 \pi}{4}\right)$

A = 1, B = 1, C = 3pi)/4, D = 0

$A m p l i t u \mathrm{de} = | A | = 1$

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

Phase shift $= - \frac{C}{B} = \frac{\frac{- 3 \pi}{4}}{1} = - \frac{3 \pi}{4}$, $\textcolor{red}{\frac{3 \pi}{4}}$ to the LEFT.

Vertical Shift $= D = 0$

graph{sin (x-((3pi)/4)) [-10, 10, -5, 5]}