document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993701>Question 993701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm in pre calculus and I need help with solving a problem. It is y=cot(x-pi/4) I need to find the period, frequency, phase shift, vertical shift, amplitude, and the asymptotes.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612970 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=612970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is y=cot(x-pi/4)\r<BR>\n" );
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document.write( "below is the graph of the equation of y = cot(x) and y = cot(x - pi/4).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/100103.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the graph of y = cot(x) is in orange.<BR>\n" );
document.write( "the graph of y = cot(x - pi/4) is in black.\r<BR>\n" );
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document.write( "you will see that the graph of y = cot(x - pi/4) is shifted to the right of the graph of y = cot(x) by pi/4 radians.\r<BR>\n" );
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document.write( "the normal interval of the cotangent function is 180 degrees, or pi.\r<BR>\n" );
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document.write( "this means the graph repeats every 180 degrees, or every pi radians.\r<BR>\n" );
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document.write( "interval shown for y = cot(x) is 0 to pi.<BR>\n" );
document.write( "interval shown for y = cot(x - pi/4) is pi/4 to 5pi/4.\r<BR>\n" );
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document.write( "the general form of a sinusoidal type wave is:\r<BR>\n" );
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document.write( "y = a * sin(b * (x-c)) + d or:<BR>\n" );
document.write( "y = a * cos(b * (x-c)) + d or:<BR>\n" );
document.write( "y = a * tan(b * (x-c)) + d or:<BR>\n" );
document.write( "y = a * cot(b * (x-c)) + d or:\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 shift<BR>\n" );
document.write( "d is the vertical shift.\r<BR>\n" );
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document.write( "sin and cos are sinusoidal type of wave with a period of 360 degrees because their pattern repeats every 360 degrees.\r<BR>\n" );
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document.write( "tan and cot are a sinusoidal type of wave with a period of 180 degrees because their pattern repeats every 180 degrees.\r<BR>\n" );
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document.write( "you want to find the period, frequency, phase shift, vertical shift, amplitude, and the asymptotes for the equation of y = cot(x - pi/4). \r<BR>\n" );
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document.write( "the period is 180 degrees, or pi radians.<BR>\n" );
document.write( "the frequency is 1 because it is  now shown.<BR>\n" );
document.write( "the phase shift is the same as the horizontal shift which is pi/4.<BR>\n" );
document.write( "the vertical shift is 0 because it is not shown..<BR>\n" );
document.write( "the amplitude is 1 because it is not shown.<BR>\n" );
document.write( "the asymptotes are at pi/4 and 5pi/4.\r<BR>\n" );
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