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)

Question 1070794: suppose that sine A=(3/5),cos B=(5/13)and both A and B are in the first quadrant,find sine (A+B)
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
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suppose that sine A=(3/5),cos B=(5/13)and both A and B are in the first quadrant,find sine (A+B)
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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) =  =  = .

Solved.

For similar solved problems see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topics
"Trigonometry. Formulas for trigonometric functions" and "Trigonometry: Solved problems".

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