document.write( "Question 925007: Find sinƟ if cscƟ = √2 \n" ); document.write( "
Algebra.Com's Answer #561256 by DrBeeee(684)\"\" \"About 
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Given: Using x = theta we have
\n" ); document.write( "(1) csc(x) = \"sqrt%282%29\"
\n" ); document.write( "Since sin(x) = 1/csc(x) we have
\n" ); document.write( "(3) sin(x) = \"1%2Fsqrt%282%29\"
\n" ); document.write( "It's improper to write an expression with a square root in the denominator so let's \"fix\" (3) as follows;
\n" ); document.write( "(4) sin(x) = \"%281%2Fsqrt%282%29%29%2A%28sqrt%282%29%2Fsqrt%282%29%29\" wherein we have multiplied (3) by one, thus did not change the value of sin(x). Now simple multiple the numerators of (4) and the denominators of (4) you get
\n" ); document.write( "(5) sin(x) = \"%281%2A%28sqrt%282%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29%29\"
\n" ); document.write( "Note that the denominator of (5) is
\n" ); document.write( "(6) \"sqrt%282%29%2Asqrt%282%29\" or simply
\n" ); document.write( "(7) 2
\n" ); document.write( "Therefore, in proper form we have
\n" ); document.write( "(8) sin(x) = \"sqrt%282%29%2F2\" \n" ); document.write( "
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