document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554415>Question 554415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry i'm not sure if this is the right category for this question but its for year 12 specialist maths and is on reciprocal circular functions.\r<BR>\n" );
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document.write( "the question is sketch the graph of each of the following reciprocal circular function over the given domain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sec%28x-pie%2F2%29 ALIGN=MIDDLE  ALT=\"y=sec%28x-pie%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C2pie ALIGN=MIDDLE  ALT=\"0%3Cx%3C2pie\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the < are supposed to be greater than or equal to signs\r<BR>\n" );
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document.write( "i'm not quite sure how to find the dilation factor for one and for two i know that the period is 2pie/b but is b 1 or is it pie/2?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361341 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=361341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure if i know the answer to this, but, in general, the formula for a repeating trigonometric function is:<BR>\n" );
document.write( "y = a(b(x-c)+d<BR>\n" );
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.<BR>\n" );
document.write( "the function you are describing looks like the reciprocal of the cosine function.<BR>\n" );
document.write( "as a cosine function, the formula would be:<BR>\n" );
document.write( "y = cos(x-pi/2)<BR>\n" );
document.write( "the frequency is 1<BR>\n" );
document.write( "the horizontal displacement is pi/2<BR>\n" );
document.write( "what this means is:<BR>\n" );
document.write( "when x = 0, you are taking the cosine of (-pi/2)<BR>\n" );
document.write( "when x = pi/2, you are taking the cosine of 0<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "the graph that peaks at x = 0 is the cosine(x) graph.<BR>\n" );
document.write( "the graph that peaks at x = pi/2 is the cosine(x-pi/2) graph.<BR>\n" );
document.write( "this is because:<BR>\n" );
document.write( "when x = 0, cosine(x) = cosine(0) = 1<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "when x = pi/2, cosine(x-pi/2) = cosine(0) = 1<BR>\n" );
document.write( "the graph of y = sec(x-pi/2) is the reciprocal of the graph of cos(x-pi/2)<BR>\n" );
document.write( "the graph of the cosine function of x would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the graph of the cosine function of (x-pi/2) would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x-pi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x-pi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if you superimpose the second graph on the first, you will see that there is a shift of pi/2 as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x%29%2Ccos%28x-pi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2pi%2C2pi%2C-1%2C1%2Ccos%28x%29%2Ccos%28x-pi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since sec(x) = 1/cos(x), this means that the graph of:<BR>\n" );
document.write( "y = sec(x-pi/2) can be graphed as:<BR>\n" );
document.write( "y = 1/cos(x-pi/2)<BR>\n" );
document.write( "that graph is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2pi%2C2pi%2C-5%2C5%2C1%2Fcos%28x-pi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2pi%2C2pi%2C-5%2C5%2C1%2Fcos%28x-pi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when you superimpose that graph on the graph of cos(x-pi/2) you get the following:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2pi%2C2pi%2C-5%2C5%2Ccos%28x-pi%2F2%29%2C1%2Fcos%28x-pi%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2pi%2C2pi%2C-5%2C5%2Ccos%28x-pi%2F2%29%2C1%2Fcos%28x-pi%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i'm not exactly sure what you mean by dilation factor.<BR>\n" );
document.write( "i couldn't see where it would apply in this problem.<BR>\n" );
document.write( "if you are talkin about a change in frequency which would result in a change in period, that doesn't apply to this problem as far as i can see.<BR>\n" );
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