# What are the important points to graph y=sin 2x?

Apr 17, 2018

$\left(0 , 0\right) , \left(\frac{\pi}{4} , 1\right) , \left(\frac{\pi}{2} , 0\right) , \left(\frac{3 \pi}{4} , - 1\right) , \left(\pi , 0\right)$

The graph should look something like this:
graph{sin(2x) [-2.38, 8.72, -2.907, 2.64]}

#### Explanation:

The equation is $y = \sin 2 x$, so it is in the form $y = \sin \left(b \cdot x\right)$ The period of this graph is $\frac{2 \pi}{b}$, which equals $\frac{2 \pi}{2}$ or $\pi$.
Therefore, the "important points" (quarter points) when graphing this function will be $\frac{\pi}{4}$ apart.

The amplitude of this graph is $1$, and there are no phase or vertical shifts, so the midline will be $0$, maximum $1$, and minimum $- 1$.

Unshifted sine functions follow the pattern (mid, max, mid, min, max), so the $y$-coordinates will be $\left(0 , 1 , 0 , - 1 , 0\right)$ And since the quarter points are $\left(\frac{\pi}{4}\right)$, with no phase shift, the $x$-coordinates will be $\left(0 , \frac{\pi}{4} , \frac{\pi}{2} , \frac{3 \pi}{4} , \pi\right)$.

Combining these points, the ordered pairs will be:
$\left(0 , 0\right) , \left(\frac{\pi}{4} , 1\right) , \left(\frac{\pi}{2} , 0\right) , \left(\frac{3 \pi}{4} , - 1\right) , \left(\pi , 0\right)$

The graph should look something like this:
graph{sin(2x) [-2.38, 8.72, -2.907, 2.64]}