document.write( "Question 814201: Eliminate theta from equations x = \"cosec%28theta%29\" and y = \"expr%281%2F4%29cot%28theta%29\" \n" ); document.write( "
Algebra.Com's Answer #490184 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Eliminate theta from equations x = \"cosec%28theta%29\" and y = \"expr%281%2F4%29cot%28theta%29\"
\n" ); document.write( "
\r\n" );
document.write( "Draw a right triangle and mark an angle q\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We look at the first equation\r\n" );
document.write( "\r\n" );
document.write( "x = \"cosec%28theta%29\"\r\n" );
document.write( "\r\n" );
document.write( "Since the cosecant is the hypotenuse over the opposite, and\r\n" );
document.write( "since x can be written as \"x%2F1\" and x = \"cosec%28theta%29\",\r\n" );
document.write( "we can put x as the length of the hypotenuse and 1 as the \r\n" );
document.write( "length of the opposite.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And by the Pythagorean theorem we can get the adjacent side\r\n" );
document.write( "\r\n" );
document.write( "     c² = a² + b²\r\n" );
document.write( "     x² = a² + 1²\r\n" );
document.write( "     x² = a² + 1\r\n" );
document.write( " x² - 1 = a²\r\n" );
document.write( "\r\n" );
document.write( "√x² - 1 = √a²\r\n" );
document.write( "\r\n" );
document.write( "√x² - 1 = a\r\n" );
document.write( "\r\n" );
document.write( "We label the length of the adjacent side\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we look at the second equation\r\n" );
document.write( "\r\n" );
document.write( "y = \"expr%281%2F4%29cot%28theta%29\"\r\n" );
document.write( "\r\n" );
document.write( "The cotangent is the adjacent over the opposite, so we substitute\r\n" );
document.write( "\"expr%28sqrt%28x%5E2-1%29%2F1%29%29\" for cot(q) or just \"sqrt%28x%5E2-1%29\".\r\n" );
document.write( "\r\n" );
document.write( "in the second equation:\r\n" );
document.write( "\r\n" );
document.write( "y = \"expr%281%2F4%29sqrt%28x%5E2-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );