document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73942>Question 73942</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh>Algebra and Trigonomerty</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of cos^-1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%284PI%2F3%29%29 ALIGN=MIDDLE  ALT=\"%28cos%284PI%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the possible answers are <BR>\n" );
document.write( "a.  -PI/3<BR>\n" );
document.write( "b.   PI/3<BR>\n" );
document.write( "c.   2PI/3<BR>\n" );
document.write( "d.   4PI/3\r<BR>\n" );
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document.write( "Thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52985 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=52985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The inverse cosine looks like this: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large cos^{-1}(x)\"> <BR>\n" );
document.write( "This function literally undoes the cosine function. If I plug in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \theta=60\"> degrees into <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large cos(\theta)\"> I get a value of 1/2 (ie <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large cos(60)=\frac{1}{2}\"> If I take the inverse cosine of 1/2 I get 60. However, since the range of inverse cosine is [0,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \pi\">], we need to find a co-angle that is in the interval [0,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \pi\">] (in other words  we need to reduce <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{4\pi}{3}\">.  So lets subtract  from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{4\pi}{3}\"> from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2\pi\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 2\pi-\frac{4\pi}{3}=\frac{2\pi}{3}\"><BR>\n" );
document.write( "So <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large cos^{-1}(cos(\frac{2\pi}{3}))=\frac{2\pi}{3}\"><BR>\n" );
document.write( "Note: if we evaluated <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large cos^{-1}(cos(\frac{4\pi}{3}))\"> we would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large cos^{-1}(cos(\frac{4\pi}{3}))=\frac{2\pi}{3}\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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