document.write( "Question 1065128: Suppose that beta is an acute angle , greater than 0 but less than 90. Compute the exact value of all of the trigonometric values of beta, given that tan beta = 3. \n" ); document.write( "

Algebra.Com's Answer #680265 by KMST(5328) $\"\"$ $\"About$

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For a right triangle with an angle measuring $\"beta\"$ ,
\n" ); document.write( " $\"tan%28beta%29\"$ = opposite leg/adjacent leg.
\n" ); document.write( "If we draw such a triangle with legs measuring $\"3\"$ and $\"1\"$ on angle $\"beta\"$ ,
\n" ); document.write( "it would look like this:
\n" ); document.write( "

$\"x%5E2=1%5E2%2B3%5E2=1%2B3\"$ <---> $\"x=sqrt%2810%29\"$ as per the Pythagorean theorem.
\n" ); document.write( "For that triangle, we can calculate:
\n" ); document.write( " $\"sin%28beta%29=3%2Fsqrt%2810%29=3sqrt%2810%29%2F10\"$
\n" ); document.write( " $\"cos%28beta%29=1%2Fsqrt%2810%29=sqrt%2810%29%2F10\"$
\n" ); document.write( " $\"cot%28beta%29=1%2Ftan%28beta%29=1%2F3\"$
\n" ); document.write( " $\"sec%28beta%29=1%2Fcos%28beta%29\"$ $\"%22=%22\"$ $\"1%2F%28%281%2Fsqrt%2810%29%29%29\"$ $\"%22=%22\"$ $\"sqrt%2810%29\"$
\n" ); document.write( " $\"csc%28beta%29=1%2Fsin%28beta%29\"$ $\"%22=%22\"$ $\"1%2F%28%283%2Fsqrt%2810%29%29%29\"$ $\"%22=%22\"$ $\"sqrt%2810%29%2F3\"$ \n" ); document.write( "

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