SOLUTION: suppose that sine A=(3/5),cos B=(5/13)and both A and B are in the first quadrant,find sine (A+B)

Use the "addition formula for sine":

sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B)     (*)


It is one of fundamental formulas of Trigonometry. You can find it in any serious Trigonometry textbook. 
Also see the lesson  Addition and subtraction formulas  in this site.


To use it, you must know cos(A) and sin(B) in addition to given sin(A) = 3/5  and cos(B) = 5/13.

It is easy to calculate:


1)  cosA) =  =  =  =  = .


2)  sin(B) =  =  =  =  = .


Now you have EVERYTHING to use the formula (*):

sin(A + B) =  =  = .