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

Jun 15, 2015

These are three steps (transformations) that you can apply in every order you want,and you'll obtain $y = - \sin \left(2 x\right)$.

#### Explanation:

1. Start graphing the trig function you know, $y = \sin \left(x\right)$.

graph{sinx [-10, 10, -5, 5]}

1. Doubling the argument you have a compression in the period, that means that the function double the frequency: if we had the solutions in $0 , \pi , 2 \pi , 3 \pi , \ldots$ now we have solutions in $0 , \frac{\pi}{2} , \pi , \frac{3}{2} \pi , 2 \pi , \ldots$

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

1. The minus sign in front of the function is a reflection on the x-axis, so for each point of the function $\left(x , y\right) \to \left(x , - y\right)$:

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