Question 1070794
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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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<pre>
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  <A HREF = http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>  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) = {{{sqrt(1-sin^2(A))}}} = {{{sqrt(1-(3/5)^2)}}} = {{{sqrt(1-9/25)}}} = {{{sqrt(16/25)}}} = {{{4/5}}}.


2)  sin(B) = {{{sqrt(1-cos^2(B))}}} = {{{sqrt(1-(5/13)^2)}}} = {{{sqrt(1-25/169)}}} = {{{sqrt(144/169)}}} = {{{12/13}}}.


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

sin(A + B) = {{{(3/5)*(5/13) + (4/5)*(12/13)}}} = {{{15/65 + 48/65}}} = {{{63/65}}}.
</pre>

Solved.



For similar solved problems see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Calculating-trigonometric-functions-of-angles.lesson>Calculating trigonometric functions of angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Selected-problems-from-the-archive-on-calculating-trig-functions-of-angles.lesson>Advanced problems on calculating trigonometric functions of angles</A>

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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