# How do you graph y=2sin(x - pi)?

Aug 28, 2015

Sketch $y = \sin \left(x\right)$ then redraw replacing each $y$ coordinate with $\left(- 2\right) \times y$

#### Explanation:

$\sin \left(x - \pi\right) = - \sin \left(x\right)$
$\Rightarrow 2 \sin \left(x - \pi\right) = - 2 \sin \left(x\right)$

The graph of ${y}_{1} = - 2 \sin \left(x\right)$ is identical to the graph of ${y}_{2} = \sin \left(x\right)$ except for any value of $x$, ${y}_{1} = \left(- 2\right) \cdot {y}_{1}$

Graph of $\sin \left(x\right)$
graph{sin(x) [-6.33, 13.67, -4.88, 5.12]}

Graph of $- 2 \sin \left(x\right)$
graph{-2sin(x) [-6.33, 13.67, -4.88, 5.12]}