Finding the Antinodes on a Waveform

[tristancohn]

i have a waveform:
y2(x)= sin(x*1.2)+sin(x*1.8)

the first 6 nodes, meaning the parts of the wave where y2=0 come up on my graph at around x =

2.094
4.189
5.236
6.283
8.377
10.471

you can find the nodes easily (where y2=0) with either x = n*pi/(1.5) or x = (2n+1)*(pi/0.6), where n = 0, 1,2 3, and so on.

what I really want to find is the antinodes (peaks) of y2, similar to on this graph where the line turns black:

http://upload.wikimedia.org/wikipedi...ative_line.gif

which are at around x =

1.006
2.979
4.665
5.808
7.492
9.466

I know that the antinodes for y2 come up at 1.8*COS(1.8*x)+1.2*COS(1.2*x)=0
but i just can't find a clean way of finding them.