# How do you graph 1/2sin(x-pi)?

Apr 18, 2015

Observing the equation of your function you can deduce a lot of things.
Considering: $y = \frac{1}{2} \sin \left(1 \cdot x - \pi\right)$ you have a sine curve with:

1]
The $1$ in front of $x$ (indicated as $k$) allows you to evaluate the length $\lambda$ of your sine curve; $k = \frac{2 \pi}{\lambda}$ or $1 = \frac{2 \pi}{\lambda}$ and $\lambda = 2 \pi$;

2]
The $\frac{1}{2}$ is the Amplitude of your sine curve (maximum height);

3]
$- \pi$ in the argument of $\sin$ means that your sine is "moved" starting at a value that is $\sin \left(- \pi\right)$ when $x = 0$; consequently it will start not "going up" as the normal sine functions but down: