sum of two periodic functions

[help_me]

i have to investigate the sum of two periodic functions with the same period and amplitude

e.g. f(x) 2 sin x and g(x) 2 cos x

so then i would go h(x) = 2 sin x + 2 cos x

but i don't really know what to do after that

i have to make general observations, predictions, and generalizations, and justify them

i changed the h(x) 2 sin x + 2 cos x to a normal periodic function, and i got y = 2.828 cos (x – ?/4)

i did the same thing to a couple more functions, and i have a couple of generalizations. i wrote that the period always stays the same and the amplitude of the new function is the amplitude of the old function multiplied by 1.414

but the trouble is, they aren't exactly brilliant generalizations

can anyone help me?

also, i apologise if i have put this in the wrong section. i didn't really know what type of math it was

oh and also, what happens when i stick a phase shift in both of the first two equations. i really can't figure it out

and why does the period always stay the same?

 

[skeeter]

actually, you made a couple of good generalizations ... go to the link to investigate further.