document.write( "Question 324168: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigometric function.\r
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Algebra.Com's Answer #232001 by jim_thompson5910(35256) $\"\"$ $\"About$

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If you draw a triangle, you'll find that the two legs are 'x' and '1' which will make the hypotenuse to be $\"sqrt%28x%5E2%2B1%29\"$ . The opposite leg is 'x' and the adjacent leg is '1' which means that $\"tan%28theta%29=x%2F1=x\"$ or simply that $\"tan%28theta%29=x\"$ . Take the arctangent of both sides to get $\"theta=arctan%28x%29\"$ (note: this is a simplified view of the arctangent function)\r
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\n" ); document.write( "\n" ); document.write( "So essentially, $\"cos%28arctan%28x%29%29=cos%28theta%29\"$ . So because the adjacent side is 1 unit long and the hypotenuse is $\"sqrt%28x%5E2%2B1%29\"$ , this means that $\"cos%28theta%29=1%2Fsqrt%28x%5E2%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Again, a drawing really helps you see why this is true. \n" ); document.write( "

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