document.write( "Question 33858: cos theta = 5/12 and tan theta is negative, find the exact valcue for sin theta. \n" ); document.write( "

Algebra.Com's Answer #168823 by jsmallt9(3758) $\"\"$ $\"About$

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cos(x) = adj/hyp
\n" ); document.write( "sin(x) = opp/hyp
\n" ); document.write( "tan(x) = opp/adj

\n" ); document.write( "We are given that cos(x) = 5/12 so we can use 5 for the adjacent side and 12 for the hypotenuse. By the Pythagorean Theorem, $\"%28adj%29%5E2+%2B+%28opp%29%5E2+=+%28hyp%29%5E2\"$ so:
\n" ); document.write( " $\"5%5E2+%2B+%28opp%29%5E2+=+12%5E2\"$
\n" ); document.write( "Simplifying we get:
\n" ); document.write( " $\"25+%2B+%28opp%29%5E2+=+144\"$
\n" ); document.write( "Subtracting 25 from each side we get:
\n" ); document.write( " $\"%28opp%29%5E2+=+119\"$
\n" ); document.write( "Finding the square root of each side we get:
\n" ); document.write( " $\"abs%28opp%29+=+sqrt%28119%29\"$
\n" ); document.write( "Since tan(x) is negative and tan(x) is opp/hyp and the hypotenuse is always positive, the opposite side must be negative. So:
\n" ); document.write( " $\"opp+=+-sqrt%28119%29\"$
\n" ); document.write( "and so, since sin(x) = opp/hyp:
\n" ); document.write( " $\"sin%28x%29+=+%28-sqrt%28119%29%29%2F12\"$ \n" ); document.write( "

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