document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582305>Question 582305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with the following questions<BR>\n" );
document.write( "1. Determine the value of the following expression without using a calculator?<BR>\n" );
document.write( "tan210degrees x sin 240 degrees x cos 180 degrees divided by 405 degrees sin (-225degrees)<BR>\n" );
document.write( "2. If tan 25degreees = a, determine in terms of a the value of:<BR>\n" );
document.write( "tan205degrees - tan115degrees divided by tan245degrees + tan335degrees. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372262 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The trigonometric functions of angles in the second, third and fourth quadrants have the same absolute value as the trigonometric functions of a reference angle in the first quadrant. The reference angle is a reflection on one of the axes (x axis or y axis, or on the origin.<BR>\n" );
document.write( "The trigonometric functions of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%5Eo ALIGN=MIDDLE  ALT=\"30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%5Eo ALIGN=MIDDLE  ALT=\"60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, are all you need when they say \"without using a calculator.\"<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%5Eo=180%5Eo%2B30%5Eo ALIGN=MIDDLE  ALT=\"210%5Eo=180%5Eo%2B30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28210%5Eo%29=tan%2830%5Eo%29=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"tan%28210%5Eo%29=tan%2830%5Eo%29=sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%5Eo=180%5Eo%2B60%5Eo ALIGN=MIDDLE  ALT=\"240%5Eo=180%5Eo%2B60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28240%5Eo%29=-sin%2860%5Eo%29=-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28240%5Eo%29=-sin%2860%5Eo%29=-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28180%5Eo%29=-1 ALIGN=MIDDLE  ALT=\"cos%28180%5Eo%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I don't know what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=405%5Eo ALIGN=MIDDLE  ALT=\"405%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > is doing, all by itself in your problem. I expected to see some trigonometric function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=405%5Eo ALIGN=MIDDLE  ALT=\"405%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, not just the angle measure. In any case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=405%5Eo=360%5Eo%2B45%5Eo ALIGN=MIDDLE  ALT=\"405%5Eo=360%5Eo%2B45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the trigonometric functions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=405%5Eo ALIGN=MIDDLE  ALT=\"405%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the same as for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (They are co-terminal angles).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-225%5Eo%2B180%5Eo=-45%5Eo ALIGN=MIDDLE  ALT=\"-225%5Eo%2B180%5Eo=-45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28-225%5Eo%29=-sin%28-45%5Eo%29=-%28-sin%2845%5Eo%29%29=sin%2845%5Eo%29=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28-225%5Eo%29=-sin%28-45%5Eo%29=-%28-sin%2845%5Eo%29%29=sin%2845%5Eo%29=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2825%5Eo%29=a ALIGN=MIDDLE  ALT=\"tan%2825%5Eo%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65%5Eo%2B25%5Eo=90%5Eo ALIGN=MIDDLE  ALT=\"65%5Eo%2B25%5Eo=90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2865%5Eo%29=1%2Ftan%2825%5Eo%29=1%2Fa ALIGN=MIDDLE  ALT=\"tan%2865%5Eo%29=1%2Ftan%2825%5Eo%29=1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "From there you can find the tangents of angles that have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65%5Eo ALIGN=MIDDLE  ALT=\"65%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5Eo ALIGN=MIDDLE  ALT=\"25%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > as reference angle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=205%5Eo=180%5Eo%2B25%5Eo ALIGN=MIDDLE  ALT=\"205%5Eo=180%5Eo%2B25%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28205%5Eo%29=tan%2825%5Eo%29=a ALIGN=MIDDLE  ALT=\"tan%28205%5Eo%29=tan%2825%5Eo%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=115%5Eo=180%5Eo-65%5Eo ALIGN=MIDDLE  ALT=\"115%5Eo=180%5Eo-65%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28115%5Eo%29=-tan%2865%5Eo%29=-1%2Fa ALIGN=MIDDLE  ALT=\"tan%28115%5Eo%29=-tan%2865%5Eo%29=-1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=245%5Eo=180%5Eo%2B65%5Eo ALIGN=MIDDLE  ALT=\"245%5Eo=180%5Eo%2B65%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28245%5Eo%29=tan%2865%5Eo%29=1%2Fa ALIGN=MIDDLE  ALT=\"tan%28245%5Eo%29=tan%2865%5Eo%29=1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=335%5Eo=360%5Eo-25%5Eo ALIGN=MIDDLE  ALT=\"335%5Eo=360%5Eo-25%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28335%5Eo%29=tan%28-25%5Eo%29=-tan%2825%5Eo%29=-a ALIGN=MIDDLE  ALT=\"tan%28335%5Eo%29=tan%28-25%5Eo%29=-tan%2825%5Eo%29=-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );