document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128737>Question 1128737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question Part<BR>\n" );
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document.write( "Find the exact value of the expression in terms of x with the help of a reference triangle. <BR>\n" );
document.write( "sin(cos&#8722;1(3 &#8722; x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745294 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the expression \"sin(cos-1(3 - x))\"<BR>\n" );
document.write( "the \"cos-1\" or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22cos%22%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%22cos%22%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > part refers to the inverse cosine function,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E%28-1%29%283-x%29 ALIGN=MIDDLE  ALT=\"cos%5E%28-1%29%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > , between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(or between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > if you want to visualize angles in degrees)<BR>\n" );
document.write( "whose cosine is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-x ALIGN=MIDDLE  ALT=\"3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those angles would have a non-negative sine, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28cos%5E%28-1%29%283-x%29%29%3E=0 ALIGN=MIDDLE  ALT=\"sin%28cos%5E%28-1%29%283-x%29%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Using the trigonometric identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28A%29%2Bcos%5E2%28A%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28A%29%2Bcos%5E2%28A%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28cos%5E%28-1%29%283-x%29%29%2Bcos%5E2%28A%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28cos%5E%28-1%29%283-x%29%29%2Bcos%5E2%28A%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-%283-x%29%5E2 ALIGN=MIDDLE  ALT=\"sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-%283-x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-%289-6x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-%289-6x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-9%2B6x-x%5E2 ALIGN=MIDDLE  ALT=\"sin%5E2%28cos%5E%28-1%29%283-x%29%29=1-9%2B6x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28cos%5E%28-1%29%283-x%29%29=-8%2B6x-x%5E2 ALIGN=MIDDLE  ALT=\"sin%5E2%28cos%5E%28-1%29%283-x%29%29=-8%2B6x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We are looking for a non-negative result, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28cos%5E%28-1%29%283-x%29%29=highlight%28sqrt%28-8%2B6x-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"sin%28cos%5E%28-1%29%283-x%29%29=highlight%28sqrt%28-8%2B6x-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOTE:<BR>\n" );
document.write( "Of course <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E%28-1%29%283-x%29 ALIGN=MIDDLE  ALT=\"cos%5E%28-1%29%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not defined as a real number for all values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=3-x%3C=1 ALIGN=MIDDLE  ALT=\"-1%3C=3-x%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=x%3C=4 ALIGN=MIDDLE  ALT=\"2%3C=x%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the domain of the function,<BR>\n" );
document.write( "but that is probably not expected as part of the answer. </SPAN>\n" );
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