document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077833>Question 1077833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sec(5&#960;/3)*tan(5&#960;/4)-cot(2&#960;/3)*sin(-&#960;/3)<BR>\n" );
document.write( "Evaluate each expression and simplyfy.<BR>\n" );
document.write( "Can someone please help me? Thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692364 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=692364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) If you know (or figure out, or look up)<BR>\n" );
document.write( "the values of the main trigonometric functions<BR>\n" );
document.write( "(cosine, sine, and tangent)<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you are 1/3 of the way to the answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C4%2Ctheta%2Ccosine%2C+sine%2C+tangent%2C%0D%0Api%2F4%2Csqrt%282%29%2F2%2Csqrt%282%29%2F2%2C1%2C%0D%0Api%2F3%2C1%2F2%2Csqrt%283%29%2F2%2Csqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "2) You need to know some trigonometric identities that are really definitions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29=1%2Ftan%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29=1%2Ftan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29=1%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29=1%2Fcos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "3) You also need to understand the relation between<BR>\n" );
document.write( "angles in other quadrants and<BR>\n" );
document.write( "their symmetrical first quadrant reference angles.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.2%2C1.2%2C-1.2%2C1.2%2Cgrid%280%29%2C%0D%0Ared%28circle%280%2C0%2C1%29%29%2Carrow%280%2C0%2C1.2%2C0.8%29%2C%0D%0Aarrow%280%2C0%2C-1.2%2C0.8%29%2Carrow%280%2C0%2C-1.2%2C-0.8%29%2C%0D%0Aarrow%280%2C0%2C1.2%2C-0.8%29%2Carc%280%2C0%2C1%2C1%2C-33.7%2C0%29%2C%0D%0Alocate%280.36%2C0.2%2Ctheta%29%2Carc%280%2C0%2C1%2C1%2C180%2C213.7%29%2C%0D%0Alocate%28-0.4%2C0.2%2Ctheta%29%2Carc%280%2C0%2C1.2%2C1.2%2C0%2C33.7%29%2C%0D%0Alocate%280.45%2C-0.1%2Ctheta%29%2Carc%280%2C0%2C1.2%2C1.2%2C146.3%2C180%29%2C%0D%0Alocate%28-0.5%2C-0.1%2Ctheta%29%2Carc%280%2C0%2C1.8%2C1.8%2C180%2C360%29%2C%0D%0Alocate%28-0.63%2C0.63%2Cpi%29%2Ctriangle%28-0.9%2C0%2C-0.93%2C0.05%2C-0.87%2C0.05%29%2C%0D%0Ared%28arc%280%2C0%2C1.4%2C1.4%2C213.7%2C360%29%29%2Clocate%280.07%2C0.63%2Cred%28pi-theta%29%29%2C%0D%0Ared%28triangle%28-0.58%2C0.39%2C-0.54%2C0.39%2C-0.58%2C0.43%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Foe example (and relevant to the problem)<BR>\n" );
document.write( "the diagram shows you that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%285%2C4%2CAngle%2C%22cosine+=%22%2C+%22sine+=%22%2C+%22tangent+=%22%2C%0D%0Api-theta%2C-cos%28theta%29%2C+sin%28theta%29%2C+-tan%28theta%29%2C%0D%0Api%2Btheta%2C-cos%28theta%29%2C+-sin%28theta%29%2C+tan%28theta%29%2C%0D%0A2pi-theta%2Ccos%28theta%29%2C+-sin%28theta%29%2C+-tan%28theta%29%2C%0D%0A-theta%2Ccos%28theta%29%2C+-sin%28theta%29%2C+-tan%28theta%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "There are diagrams, tables and charts that can help you.<BR>\n" );
document.write( "Your textbook probably has then.<BR>\n" );
document.write( "Your teacher probably handed out that kind of help.<BR>\n" );
document.write( "You can find them online searching for \"trig identities.\"<BR>\n" );
document.write( "Wikipedia has a nice diagram, and a table.<BR>\n" );
document.write( "However, you can figure out the answers by yourself,<BR>\n" );
document.write( "with the Pythagorean theorem.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3 ALIGN=MIDDLE  ALT=\"pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > think of half of an equilateral triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1.1%2C1.1%2C-0.2%2C1.8%2C%0D%0Agreen%28triangle%280%2C0%2C1%2C0%2C0%2C1.732%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C0.05%2C0.05%29%29%2C%0D%0Atriangle%28-1%2C0%2C1%2C0%2C0%2C1.732%29%2Clocate%280.02%2C0.8%2Ch%29%2C%0D%0Alocate%280.35%2C0.1%2C%221+%2F+2%22%29%2Clocate%280.45%2C0.88%2C1%29%2C%0D%0Ared%28arc%280%2C1.732%2C0.6%2C0.6%2C60%2C90%29%29%2C%0D%0Ared%28arc%281%2C0%2C0.65%2C0.65%2C180%2C240%29%29%2C%0D%0Alocate%280.05%2C1.45%2Cred%28pi%2F6%29%29%2C%0D%0Alocate%280.75%2C0.23%2Cred%28pi%2F3%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The Pythagorean theorem lets you figure out<BR>\n" );
document.write( "the length of the long leg as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"h=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F3=60%5Eo ALIGN=MIDDLE  ALT=\"pi%2F3=60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we have the trigonometric ratios<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3%29=1%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F3%29=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sin%28pi%2F3%29=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28pi%2F6%29=%28sqrt%283%29%2F2%29%2F%281%2F2%29=sqrt%283%29 ALIGN=MIDDLE  ALT=\"tan%28pi%2F6%29=%28sqrt%283%29%2F2%29%2F%281%2F2%29=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > think of half of a square. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );