document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203961>Question 1203961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28x%29+=+4+%2F+5+ ALIGN=MIDDLE  ALT=\"+tan%28x%29+=+4+%2F+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > then, without a calculator, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28pi+%2F+2+-+x%29+ ALIGN=MIDDLE  ALT=\"tan%28pi+%2F+2+-+x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Write your answer as a fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839906 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "List of common trig identities<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf\">https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf</a>\r<BR>\n" );
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document.write( "The identity we'll be using is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28pi%2F2+-+x%29+=+cot%28x%29 ALIGN=MIDDLE  ALT=\"tan%28pi%2F2+-+x%29+=+cot%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it is found at the bottom of page 2 under the subsection \"Cofunction Formulas\".\r<BR>\n" );
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document.write( "Cotangent is the reciprocal of tangent, meaning that if tan(x) = 4/5, then cot(x) = 5/4.<BR>\n" );
document.write( "This then leads back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28pi%2F2+-+x%29+=+5%2F4 ALIGN=MIDDLE  ALT=\"tan%28pi%2F2+-+x%29+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is another approach.\r<BR>\n" );
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document.write( "Draw out a right triangle with these properties:<BR>\n" );
document.write( "opposite = 4<BR>\n" );
document.write( "adjacent = 5<BR>\n" );
document.write( "theta = reference angle\r<BR>\n" );
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document.write( "We are then effectively given that tan(theta) = 4/5<BR>\n" );
document.write( "The expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+-+theta ALIGN=MIDDLE  ALT=\"pi%2F2+-+theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the other acute angle of this right triangle.<BR>\n" );
document.write( "This is because the two acute angles add to pi/2 radians (aka 90 degrees). The acute angles are complementary.\r<BR>\n" );
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document.write( "With reference to angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+-+theta ALIGN=MIDDLE  ALT=\"pi%2F2+-+theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the positions of \"opposite\" and \"adjacent\" swap places.<BR>\n" );
document.write( "This will mean that we have:<BR>\n" );
document.write( "opposite = 5<BR>\n" );
document.write( "adjacent = 4<BR>\n" );
document.write( "pi/2 - theta = reference angle\r<BR>\n" );
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document.write( "Therefore, tan(pi/2 - theta) = opposite/adjacent = <font color=red>5/4</font>\r<BR>\n" );
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document.write( "Here is a diagram of what I refer to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-3%2C-3%2C3%2C3%29%2C%0D%0Aline%283%2C3%2C3%2C-3%29%2C%0D%0Aline%283%2C-3%2C-3%2C-3%29%2C%0D%0Aline%283-0.5%2C-3%2C3-0.5%2C-3%2B0.5%29%2C%0D%0Aline%283-0.5%2C-3%2B0.5%2C3%2C-3%2B0.5%29%2C%0D%0Alocate%283.5%2C0%2C%224%22%29%2C%0D%0Alocate%280%2C-3.2%2C%225%22%29%2C%0D%0Alocate%283-1.2%2C3-1.2%2Cpi%2F2-theta%29%2C%0D%0Alocate%28-3%2B0.8%2C-3%2B0.5%2Ctheta%29%2C%0D%0Alocate%28-4.5%2C-4%2Cmatrix%281%2C2%2C%22Diagram%22%2C%22not%22%29%29%2C%0D%0Alocate%28-4.5%2C-4.5%2Cmatrix%281%2C2%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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