document.write( "Question 1003933: can someone give me some guidance on how to rewrite as an algebraic expression\r
\n" ); document.write( "\n" ); document.write( "sin(arctan(x))=sin theta? \n" ); document.write( "

Algebra.Com's Answer #620541 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Let $\"alpha\"$ = arctan(x).\r
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\n" ); document.write( "\n" ); document.write( "Then $\"tan%28alpha%29\"$ = x = $\"sin%28alpha%29%2Fcos%28alpha%29\"$             -----> \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ = $\"sin%5E2%28alpha%29%2Fcos%5E2%28alpha%29\"$ = $\"sin%5E2%28alpha%29%2F%281+-+sin%5E2%28alpha%29%29\"$     -----> \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2A%281+-+sin%5E2%28alpha%29%29\"$ = $\"sin%5E2%28alpha%29\"$         ----->\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ - $\"x%5E2\"$ . $\"sin%5E2%28alpha%29\"$ = $\"sin%5E2%28alpha%29\"$       ----->\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ = $\"%281%2Bx%5E2%29\"$ . $\"sin%5E2%28alpha%29\"$                 -----> \r
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\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28alpha%29\"$ = $\"%28x%5E2%29%2F%281+%2B+x%5E2%29\"$ ,\r
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\n" ); document.write( "\n" ); document.write( " $\"sin%28alpha%29\"$ = $\"sqrt%28%28x%5E2%29%2F%281%2Bx%5E2%29%29\"$ = +/- $\"%28abs%28x%29%29%2F%28sqrt%281%2Bx%5E2%29%29\"$ = $\"x%2F%28sqrt%281%2Bx%5E2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Finally,   sin(arctan(x)) = $\"x%2F%28sqrt%281%2Bx%5E2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Is this what you want?\r
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