difference between atan2(x,y) and atan(x/y)

>maxplanck wrote:
>> I'm a bit stumped here, maybe someone can help me out?
>> 
>> y = atan (sin(2*pi*x) / cos(2*pi*x)); 
>> 
>> s = atan2 (sin(2*pi*x) , cos(2*pi*x));
>> 
>> I would expect y and s to be equal, but they're not.
>> 
>> Most surprising to me is that the maximum value of s appears to be pi,
>> despite the fact that the limit of atan2(a,b) as a/b->infinity is pi/2
>> (right?)
>> 
>> Can anyone clue me in as to why my expectations are being defied here? 
I
>> think the root of my misunderstanding lies in my not understanding the
>> differences between atan(a/b) and atan2(a,b).
>> 
>> Thanks, any help is much appreciated
>
>How much trig do you remember? Can you simplify sin(x)/cos(x)? Are you 
>familiar with the concept of "principal value"?
>
>Jerry
>-- 
>Engineering is the art of making what you want from things you can get.

sin=opp/hyp
cos=adj/hyp
tan=opp/adj

sin/cos = (opp/hyp)*(hyp/adj) = opp/adj = tan

I just read up on principal value, i think that i understand the concept.


Thanks for all the responses guys (both the serious and the funny ones =).