# How do you graph y=sin2x?

Aug 9, 2018

Below

#### Explanation:

When written in the form $y = a \sin \left(n x + b\right) + c$ where
$a$ is the amplitude
$n$ is used to find the period of the function
$b$ is to find the shift to the left or right by $b$ units
$c$ is to find the shift upwards or downwards by $c$ units

Looking at $y = \sin 2 x$, it is clear that:
$a = 1$
$b = 0$
$\text{period} = \frac{2 \pi}{n} = \frac{2 \pi}{2} = \pi$
$c = 0$

Therefore, $y = \sin 2 x$ is basically the $y = \sin x$ graph but instead of having a period of $2 \pi$, it has a period of $\pi$. So what that means is that in $y = \sin 2 x$, you will see two $\sin x$ graphs occurring.

graph{sin(2x) [-10, 10, -5, 5]}