document.write( "Question 1074974: find the exact value of the trigonometric function given that sin u= 8/17 and cos v= -9/47 \r
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Algebra.Com's Answer #689684 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sin%5E2%28u%29=64%2F289\"$
\n" ); document.write( " $\"cos%5E2%28u%29=1-sin%5E2%28u%29\"$
\n" ); document.write( " $\"cos%5E2%28u%29=1-64%2F289\"$
\n" ); document.write( " $\"cos%5E2%28u%29=289%2F289-64%2F289\"$
\n" ); document.write( " $\"cos%5E2%28u%29=225%2F289\"$
\n" ); document.write( " $\"cos%28u%29=15%2F17\"$ or $\"cos%28u%29=-15%2F17\"$
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\n" ); document.write( "Similarly,
\n" ); document.write( " $\"cos%5E2%28v%29=81%2F2209\"$
\n" ); document.write( " $\"sin%5E2%28v%29=1-cos%5E2%28v%29\"$
\n" ); document.write( " $\"sin%5E2%28v%29=1-81%2F2209\"$
\n" ); document.write( " $\"sin%5E2%28v%29=2209%2F2209-81%2F2209\"$
\n" ); document.write( " $\"sin%5E2%28v%29=2128%2F2209\"$
\n" ); document.write( " $\"sin%28v%29=sqrt%282128%29%2F47\"$ or $\"sin%28v%29=-sqrt%282128%29%2F47\"$
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\n" ); document.write( "So then,
\n" ); document.write( " $\"csc%28u-v%29=1%2Fsin%28u-v%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"sin%28u-v%29=sin%28u%29cos%28v%29-sin%28v%29cos%28u%29\"$
\n" ); document.write( "So there are 4 possible solutions.
\n" ); document.write( "1. $\"cos%28u%29\"$ positive, $\"sin%28v%29\"$ positive
\n" ); document.write( "2. $\"cos%28u%29\"$ positive, $\"sin%28v%29\"$ negative
\n" ); document.write( "3. $\"cos%28u%29\"$ negative, $\"sin%28v%29\"$ positive
\n" ); document.write( "4. $\"cos%28u%29\"$ negative, $\"sin%28v%29\"$ negative\r
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\n" ); document.write( "I'll do case #1, you do the others the same way.
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\n" ); document.write( " $\"sin%28u-v%29=sin%28u%29cos%28v%29-sin%28v%29cos%28u%29\"$
\n" ); document.write( " $\"sin%28u-v%29=%288%2F17%29%28-9%2F47%29-%28sqrt%282128%29%2F47%29%2815%2F17%29\"$
\n" ); document.write( " $\"sin%28u-v%29=%28-72%2F799%29-%2815%2F799%29%28sqrt%282128%29%29\"$
\n" ); document.write( " $\"sin%28u-v%29=-%2872%2B15sqrt%282128%29%29%2F799\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"csc%28u-v%29=-799%2F%2872%2B15sqrt%282128%29%29\"$
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