document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169143>Question 1169143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't really know the topic.\r<BR>\n" );
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document.write( "Arrange the expressions in increasing order of their values. \r<BR>\n" );
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document.write( "1.cos(52.5)cos(7.5)<BR>\n" );
document.write( "2.sin(52.5)cos(7.5)<BR>\n" );
document.write( "3.sin(52.5)sin(7.5)<BR>\n" );
document.write( "4.cos(52.5)sin(7.5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793783 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I'm guessing we are supposed to answer this question using estimation and our basic understanding of the sine and cosine functions -- rather than evaluating each expression using a calculator.<br><BR>\n" );
document.write( "The sine function is 0 at 0 degrees and increases to 1 at 90 degrees.  The increase is rapid in the beginning and slow at the end.  At 45 degrees, the sine value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is about 0.7.<br><BR>\n" );
document.write( "So useful estimations are sin(7.5) = 0.1 and sin(52.5) = 0.8.<br><BR>\n" );
document.write( "The cosine function is 1 at 0 degrees and decreases to 0 at 90 degrees.  The decrease is very slow at first and faster at the end.  At 45 degrees, the cosine value is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or about 0.7.<br><BR>\n" );
document.write( "So useful estimations are cos(7.5) = 1 and cos(52.5) = 0.6.<br><BR>\n" );
document.write( "Therefore, we can estimate....<br><BR>\n" );
document.write( "1. cos(52.5)(cos(7.5) = (0.6)(1) = 0.6<BR>\n" );
document.write( "2. sin(52.5)(cos(7.5) = (0.8)(1) = 0.8<BR>\n" );
document.write( "3. sin(52.5)(sin(7.5) = (0.8)(0.1) = 0.08<BR>\n" );
document.write( "4. cos(52.5)(sin(7.5) = (0.6)(0.1) = 0.06<br><BR>\n" );
document.write( "Now it is easy to arrange those numbers in increasing order.<br><BR>\n" );
document.write( " </SPAN>\n" );
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