document.write( "Question 921668: given that \"cos%28x%29+=+3%2F5\", \"3pi%2F2+%3C+x+%3C+2pi\" find
\n" ); document.write( "\"cos%28x%2F2%29\", \"sin%28x%2F2%29\". \"tan%28x%2F2%29\" \n" ); document.write( "
Algebra.Com's Answer #559135 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"cos%28x%29+=+3%2F5\", \"3pi%2F2+%3C+x+%3C+2pi\" find \r\n" );
document.write( "\"cos%28x%2F2%29\", \"sin%28x%2F2%29\", and \"tan%28x%2F2%29\".\r\n" );
document.write( "\r\n" );
document.write( "Since \"3pi%2F2%3Cx%3C2pi\", dividing the three sides of the inequality by 2,\r\n" );
document.write( "\r\n" );
document.write( "\"3pi%2F4%3Cx%2F2%3Cpi\", which tells us that \"x%2F2\" is in quadrant II\r\n" );
document.write( "\r\n" );
document.write( "To find \"cos%28x%2F2%29\" will need the half-angle formulas:\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28x%2F2%29=+%22%22+%2B-+sqrt%28%281%2Bcos%28x%29%29%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "But since \"x%2F2\" is in quadrant II, its cosine is negative, so we\r\n" );
document.write( "will only use the negative sign:\r\n" );
document.write( "\r\n" );
document.write( "\"cos%28x%2F2%29=+-sqrt%28%281%2Bcos%28x%29%29%2F2%29=+-sqrt%28%281%2B3%2F5%29%2F2%29\" \r\n" );
document.write( "\r\n" );
document.write( "To simplify \"%281%2B3%2F5%29%2F2\", multiply top and bottom by 5, \"%285%2B3%29%2F10=8%2F10=4%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "---------------------\r\n" );
document.write( "\r\n" );
document.write( "To find \"sin%28x%2F2%29\" will need the half-angle formulas:\r\n" );
document.write( "\r\n" );
document.write( "\"sin%28x%2F2%29=+%22%22+%2B-+sqrt%28%281-cos%28x%29%29%2F2%29\"\r\n" );
document.write( "\r\n" );
document.write( "But since \"x%2F2\" is in quadrant II, its sine is positive, so we\r\n" );
document.write( "will only use the positive sign:\r\n" );
document.write( "\r\n" );
document.write( "\"sin%28x%2F2%29=+-sqrt%28%281-cos%28x%29%29%2F2%29=+-sqrt%28%281-3%2F5%29%2F2%29\" \r\n" );
document.write( "\r\n" );
document.write( "To simplify \"%281-3%2F5%29%2F2\", multiply top and bottom by 5, \"%285-3%29%2F10=2%2F10=1%2F5\"\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "-------------------------\r\n" );
document.write( "\r\n" );
document.write( "To find \"tan%28x%2F2%29\" there are several half-angle identities we could\r\n" );
document.write( "use.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "However I think since I already have the sine and cosine of \"x%2F2\",\r\n" );
document.write( "I'll use the quotient identity:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );