document.write( "Question 1113025: Can someone help? Thank you.
\n" ); document.write( "What is cot(csc^-1(a/b)) in terms of a and b?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #728112 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "csc is a trigonometry function cosec, which is  1/sin.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You are given that   csc(t) = \"a%2Fb\",   where \"t\"  is some angle  and  \"a\"  and  \"b\" are some real numbers.\r\n" );
document.write( "\r\n" );
document.write( "and \"they\" want you find  cot(t). \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In other words, you are given that  sin(t) = \"b%2Fa\"  (inverted ratio),\r\n" );
document.write( "\r\n" );
document.write( "and \"they\" want you find  cot(t). \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As you know  (or must know)  cot(t) = \"cos%28t%29%2Fsin%28t%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You just know the denominator  sin(t):  it is just given and is equal to  \"b%2Fa\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next step you need to do is to compute  cos(t).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is easy:  cos(t) = \"sqrt%281-sin%5E2%28t%29%29\" = \"sqrt%281-+%28b%2Fa%29%5E2%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, you answer is:  cot(t) = \"sqrt%281-%28b%2Fa%29%5E2%29%2F%28%28b%2Fa%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.   cot(csc^-1(a/b)) = cot(t) = cot(arccsc(a/b) = \"sqrt%281-%28b%2Fa%29%5E2%29%2F%28%28b%2Fa%29%29\".\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "------------
\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Is everything clear to you in this solution and in the answer ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "=============\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you still have questions, you can post them to me through the \"Thank you\" window/message/form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you do, then refer please to the problem's ID number, which is 1113025.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can find other similar solved problems in the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Evaluating trigonometric expressions \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Trigonometry: Solved problems\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );