Question 1113025
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<pre>
csc is a trigonometry function cosec, which is  1/sin.


You are given that   csc(t) = {{{a/b}}},   where "t"  is some angle  and  "a"  and  "b" are some real numbers.

and "they" want you find  cot(t). 


In other words, you are given that  sin(t) = {{{b/a}}}  (inverted ratio),

and "they" want you find  cot(t). 


As you know  (or must know)  cot(t) = {{{cos(t)/sin(t)}}}.


You just know the denominator  sin(t):  it is just given and is equal to  {{{b/a}}}.


Next step you need to do is to compute  cos(t).


It is easy:  cos(t) = {{{sqrt(1-sin^2(t))}}} = {{{sqrt(1- (b/a)^2)}}}.


Therefore, you answer is:  cot(t) = {{{sqrt(1-(b/a)^2)/((b/a))}}}.


<U>Answer</U>.   cot(csc^-1(a/b)) = cot(t) = cot(arccsc(a/b) = {{{sqrt(1-(b/a)^2)/((b/a))}}}.
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Solved.


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You can find other 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>". 



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Free of charge online textbook in ALGEBRA-II
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