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

1 Answer
Apr 17, 2018

#(0, 0), (pi/4, 1), (pi/2, 0), ((3pi)/4, -1), (pi, 0)#

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

Explanation:

The equation is #y=sin2x#, so it is in the form #y=sin(b*x)# The period of this graph is #(2pi)/b#, which equals #(2pi)/2# or #pi#.
Therefore, the "important points" (quarter points) when graphing this function will be #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 #(0,1,0,-1,0)# And since the quarter points are #(pi/4)#, with no phase shift, the #x#-coordinates will be #(0, pi/4, pi/2, (3pi)/4, pi)#.

Combining these points, the ordered pairs will be:
#(0, 0), (pi/4, 1), (pi/2, 0), ((3pi)/4, -1), (pi, 0)#

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