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

1 Answer
Jun 15, 2015

Answer:

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

Explanation:

  1. Start graphing the trig function you know, #y=sin(x)#.

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,2pi,3pi,...# now we have solutions in #0,pi/2,pi,3/2pi,2pi,...#

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 #(x,y)->(x,-y)#:

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