document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901679>Question 901679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If tan y = 0.404, where y is acute, find cos2y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546936 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=546936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you are allowed to use a calculator, then the solution should not be difficult.<BR>\n" );
document.write( "tan(y) = .404 gets you:<BR>\n" );
document.write( "y = arctan(.404) = 21.99870822 degrees.<BR>\n" );
document.write( "then 2y = 43.99741645 degrees.<BR>\n" );
document.write( "then cos(2y) = cos(43.99741645) = .7193711228\r<BR>\n" );
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document.write( "you could also have solved it as follows:\r<BR>\n" );
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document.write( "tan(y) = .404\r<BR>\n" );
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document.write( ".404 is equivalent to 101/250\r<BR>\n" );
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document.write( "the hypotenuse of a triangle with an opposite side of 101 and an adjacent side of 250 is equal to sqrt(72701)\r<BR>\n" );
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document.write( "since this is not a rational number, we'll leave it as sqrt(72701)\r<BR>\n" );
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document.write( "so we have:\r<BR>\n" );
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document.write( "tan(y) = 101/250<BR>\n" );
document.write( "cos(y) = 250/sqrt(72701)<BR>\n" );
document.write( "sin(y) = 101/sqrt(72701)\r<BR>\n" );
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document.write( "by the trigonometric identity for cos(2y), you get:\r<BR>\n" );
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document.write( "cos(2y) = cos^2(y) - sin^2(y) which becomes:\r<BR>\n" );
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document.write( "cos(2y) = 250^2/72701 - 101^2/72701 =  .7193711228\r<BR>\n" );
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document.write( "you get the same answer.\r<BR>\n" );
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document.write( "the 72701 in the denominator is really sqrt(72701)^2 which is equal to 72701.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "(250/sqrt(72701))^2 = 250^2 / sqrt(72701)^2 = 250^2 / 72701.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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