Question 1131114
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<pre>
You are given that  {{{sin(theta)}}} = {{{x/(x+1)}}},

and they want you calculate  {{{cot(theta)}}}.



First, calculate  {{{cos(theta)}}} = {{{sqrt(1-sin^2(theta))}}} = {{{sqrt(1 - (x/(x+1))^2)}}} = {{{sqrt(1-(x^2/(x^2+2x+1)))}}} = {{{sqrt((x^2 + 2x + 1 - x^2)/(x+1)^2)}}} = {{{sqrt(2x+1)/(x+1)}}}.


The last step is to calculate  {{{cot(theta)}}} = {{{cos(theta)/sin(theta)}}} = {{{((sqrt(2x+1)/(x+1)))/((x/(x+1)))}}} = {{{sqrt(2x+1)/x}}} = your answer.
</pre>

Done.


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You can find many similar solved problems in 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.