🚀 go-pugleaf

Hello,
     As some of you may or may not know when a number is pressed on 
the key pad of a telephone two tones are emitted, I wish to copy the 
resulting sound to make a autodialer but- I am told by the people in 
telecom land that the resultant frequencie is NOT the average. I know 
that SIN (x + y) = SIN(x)COS(y) + COS(x)SIN(y) but when i plot this 
on my plotting program for say the frequencies of say 1209, 657 it just 
evaluates the numbers and draws a straight line parallel to the x axis, 
is the y value of this line the resultant freq? ie:

SIN (1209 + 657) = SIN(1209)COS(657) + COS(1209)SIN(657)

I know that I should be able to figure this one out by myself but cannot 
and are getting very frustrated. Any help in the form of dummy proof 
explinations would be very much appreciated.

Al Grant

PS the question is: A) is the freq. the average?
                    B) whats the equation?