document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923726>Question 923726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Let+f+%28x%29+=+1%2Fx%5E2+%28sqrt%2825+%2B+x%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+Let+f+%28x%29+=+1%2Fx%5E2+%28sqrt%2825+%2B+x%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+and+g%28t%29+=+5+tan%28t%29+for+0+%3C+t+%3C+pi%2F2+ ALIGN=MIDDLE  ALT=\"+and+g%28t%29+=+5+tan%28t%29+for+0+%3C+t+%3C+pi%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find (f º g)(t) and simplify so that there are no radicals in the function. Write your answer in terms of sin(t) and cos(t).\r<BR>\n" );
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document.write( "(f º g)(t) = \r<BR>\n" );
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document.write( "There shouldn't be a parentheses around 25+x^2 just couldn't make it without one it seems<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Let+f+%28x%29+=+4x%2F%28sqrt%281-x%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+Let+f+%28x%29+=+4x%2F%28sqrt%281-x%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+and+g%28t%29+=+sin%28t%29+for+0+%3C+t+%3C+pi%2F2+ ALIGN=MIDDLE  ALT=\"+and+g%28t%29+=+sin%28t%29+for+0+%3C+t+%3C+pi%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find (f compose g)(t) and simplify. Write your answer in terms of sin t and cos t.\r<BR>\n" );
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document.write( "(f º g)(t) =\r<BR>\n" );
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document.write( "Please explain these<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560277 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=560277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "(f º g)(t) is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. They are just two ways of saying the same exact thing.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+1%2F%28x%5E2%2Asqrt%2825+%2B+x%5E2%29%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+1%2F%28x%5E2%2Asqrt%2825+%2B+x%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%28%28g%28t%29%29%5E2%2Asqrt%2825+%2B+%28g%28t%29%29%5E2%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%28%28g%28t%29%29%5E2%2Asqrt%2825+%2B+%28g%28t%29%29%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with g(t)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%28%285%2Atan%28t%29%29%5E2%2Asqrt%2825+%2B+%285%2Atan%28t%29%29%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > On the right side, replace all copies of g(t) with 5tan(t)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2Asqrt%2825+%2B+25%2Atan%5E2%28t%29%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2Asqrt%2825+%2B+25%2Atan%5E2%28t%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Atan%28t%29 ALIGN=MIDDLE  ALT=\"5%2Atan%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Atan%5E2%28t%29 ALIGN=MIDDLE  ALT=\"25%2Atan%5E2%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2Asqrt%2825%281+%2B+tan%5E2%28t%29%29%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2Asqrt%2825%281+%2B+tan%5E2%28t%29%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2Asqrt%2825%29%2Asqrt%281+%2B+tan%5E2%28t%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asqrt%281+%2B+tan%5E2%28t%29%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asqrt%281+%2B+tan%5E2%28t%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asqrt%28sec%5E2%28t%29%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asqrt%28sec%5E2%28t%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the trig identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Btan%5E2%28t%29+=+sec%5E2%28t%29 ALIGN=MIDDLE  ALT=\"1%2Btan%5E2%28t%29+=+sec%5E2%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asec%28t%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%2825%2Atan%5E2%28t%29%2A5%2Asec%28t%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%5E2%28t%29 ALIGN=MIDDLE  ALT=\"sec%5E2%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C+t+%3C+pi%2F2 ALIGN=MIDDLE  ALT=\"0+%3C+t+%3C+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28t%29 ALIGN=MIDDLE  ALT=\"sec%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%2825%2A%28%28sin%5E2%28t%29%29%2F%28cos%5E2%28t%29%29%29%2A5%2A%281%2Fcos%28t%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite tan & sec in terms of sine & cosine.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+1%2F%28%28125%2Asin%5E2%28t%29%29%2F%28cos%5E3%28t%29%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+1%2F%28%28125%2Asin%5E2%28t%29%29%2F%28cos%5E3%28t%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and rearrange terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28t%29%29+=+%28cos%5E3%28t%29%29%2F%28125%2Asin%5E2%28t%29%29+ ALIGN=MIDDLE  ALT=\"f%28g%28t%29%29+=+%28cos%5E3%28t%29%29%2F%28125%2Asin%5E2%28t%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the fraction (1/[a/b] = b/a)\r<BR>\n" );
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document.write( "Side Note: this only works when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28t%29+%3E+0 ALIGN=MIDDLE  ALT=\"sec%28t%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in quadrant I and IV)\r<BR>\n" );
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document.write( "Let me know if that helps or not. Thanks.\r<BR>\n" );
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document.write( "If you need more help, feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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