document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203820>Question 1203820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all exact solutions on the interval 0 ≤ x < 2𝜋.  (Enter your answers as a comma-separated list.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839662 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=839662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cot(x) + 5 = 6<BR>\n" );
document.write( "subtract 5 from both sides of the equation to get:<BR>\n" );
document.write( "cot(x) = 1<BR>\n" );
document.write( "since cot(x) = 1/tan(x), you get:<BR>\n" );
document.write( "1/tan(x) = 1<BR>\n" );
document.write( "solve for tan(x) to get:<BR>\n" );
document.write( "tan(x) = 1/1 = 1\r<BR>\n" );
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document.write( "if your calculator is set to degrees....<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "arctan(1) = 45 degrees.<BR>\n" );
document.write( "tangent is positive in the first and third quadrants.<BR>\n" );
document.write( "the equivalent angle in the third quadrant is 180 + 45 = 225 degrees.<BR>\n" );
document.write( "in the interval between 0 and 360 degrees, your angle will be 45 degrees and 225 degrees.<BR>\n" );
document.write( "here's what it looks like on a graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092202.jpg\">\r<BR>\n" );
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document.write( "if your calculator is set to radians....<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "arctan(1) = .7853981634 radians.<BR>\n" );
document.write( "tangent is positive in the first and third quadrants.<BR>\n" );
document.write( "the equivalent angle in the third wuadrant is pi + .7853981634 = 3.926990817 radians.<BR>\n" );
document.write( "in the interval between 0 and 2pi radians, your angle will be .7853981634 radians and 3.926990817 radians.<BR>\n" );
document.write( "here's what it looks like on a graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092203.jpg\">\r<BR>\n" );
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document.write( "note that .7853981634 radians is equal to .25 * pi radians which is equal to pi/4 radians, as shown on the graph.\r<BR>\n" );
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document.write( "note also that 3.926990817 radians is equal to 1.25 * pi radians which is equal to 5pi/4 radians, as shown on the graph.\r<BR>\n" );
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document.write( "note that most calculators don't handle cotangent function directly.<BR>\n" );
document.write( "my ti-84 plus is one of them.<BR>\n" );
document.write( "to solve for cotangent, it is necessary to convert cotangent to equivalent tangent function.<BR>\n" );
document.write( "as an example:<BR>\n" );
document.write( "if cotan(x) = 7, then 1/tan(x) = 7.<BR>\n" );
document.write( "solve for tan(x) to get tan(x) = 1/7.<BR>\n" );
document.write( "calculator says that x = arctan(1/7) = 8.130102354 degrees.<BR>\n" );
document.write( "that should be your angle.<BR>\n" );
document.write( "cot(8.120102354) should be equal to 7.<BR>\n" );
document.write( "since cot = 1/tan, then 1/tan(8.120102354) = 7<BR>\n" );
document.write( "use your calculator to get 1/tan(8.120102354) = 7.\r<BR>\n" );
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document.write( "the graphing software i use (desmos.com) can handle cotangent function directly, as you can see.\r<BR>\n" );
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