document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968429>Question 968429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the period of f(x) = cot(4x)+7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591792 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=591792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the normal period of cot(x) would be pi.<BR>\n" );
document.write( "this is because the graph repeats every pi units on the x-axis.<BR>\n" );
document.write( "the graph of cot(x) is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the period of cot(4x) would be pi/4.<BR>\n" );
document.write( "this is because the graph repeats every pi/4 units on the x-axis.<BR>\n" );
document.write( "the graph of cot(4x) is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "period for sine and cosine and secant and cosecant function = 2pi / frequency\r<BR>\n" );
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document.write( "frequency for sine and cosine and secant and cosecant function = 2pi / period.\r<BR>\n" );
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document.write( "period for tangent and cotangent function = pi / frequency.\r<BR>\n" );
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document.write( "frequency for tangent and cotangent function = pi / period.\r<BR>\n" );
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document.write( "in your probolem, the frequency of the cotangent function is 4.\r<BR>\n" );
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document.write( "this makes the period pi/4.\r<BR>\n" );
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document.write( "if you were given the period as pi/4, then the freq8uency would be calculated as pi / (pi/4) which would then become 4.\r<BR>\n" );
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document.write( "the general formula for repeating trigonometric functions is\r<BR>\n" );
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document.write( "y = a*sin(b*(x-c))+d\r<BR>\n" );
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document.write( "a is the amplitude.<BR>\n" );
document.write( "b is the frequency<BR>\n" );
document.write( "c is the horizontal displacement.<BR>\n" );
document.write( "d is the vertical displacement.\r<BR>\n" );
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document.write( "your equation would be shown as:\r<BR>\n" );
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document.write( "y = a*cot(b*(x-c)+d\r<BR>\n" );
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document.write( "in your equation:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = 0<BR>\n" );
document.write( "d = 7\r<BR>\n" );
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document.write( "your amplitude is 1.<BR>\n" );
document.write( "your frequency is 4<BR>\n" );
document.write( "your horizontal displacement is 0.<BR>\n" );
document.write( "your vertical displacement is 7.\r<BR>\n" );
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document.write( "vertical displacement means that your center line for the graph will be 7 units above the x-axis.\r<BR>\n" );
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document.write( "here's the graph of y = cot(4x).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C2%2C-15%2C15%2C1%2Ftan%284x%29%2C0%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C2%2C-15%2C15%2C1%2Ftan%284x%29%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "here's the graph of y = cot(4x) + 7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C2%2C-15%2C15%2C1%2Ftan%284x%29%2B7%2C7%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C2%2C-15%2C15%2C1%2Ftan%284x%29%2B7%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that the centerline for the grpah has been vertically displaced by 7 units in a positive direction.\r<BR>\n" );
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document.write( "here's a couple of references for you to ponder.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/att7/sincostan.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/att7/sincostan.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/att7/othergraphs.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/att7/othergraphs.htm</a>\r<BR>\n" );
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document.write( "note that the normal period for sine and cosine is shown as 2pi and the normal period for tangent and cotangent is shown as pi.\r<BR>\n" );
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