Question 1094865
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<pre>
1.  "x is in Quadrant IV with cos(x) = 3/5"  ====>  sin(x) = {{{sqrt(1-cos^2(x))}}} = {{{sqrt(1-(3/5)^2)}}} = {{{-4/5}}}.

    The sign is "-" since sine is negative in QIV.



2.  "y is in Quadrant III with sin(y) = {{{-2/sqrt(5)}}}"  ====>  cos(y) = {{{sqrt(1-sin^2(y))}}} = {{{sqrt(1-4/5)}}} = {{{-1/sqrt(5)}}}.

    The sign is "+" since cosine is negative in QIII.



3.  cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) = {{{(3/5)*(-1/sqrt(5)) - (-4/5)*(-2/sqrt(5))}}} = {{{-3/(5*sqrt(5)) - 8/(5*sqrt(5))}}} = {{{-11/(5*sqrt(5))}}} = {{{-11sqrt(5)/25}}}.
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To see more solved similar problems on calculating trig functions, look into 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Evaluating-trigonometric-expressions.lesson>Evaluating trigonometric expressions</A> 

in this site.


Also, &nbsp;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 topic &nbsp;"<U>Trigonometry: Solved problems</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.