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<HTML><!-- -- Copyright (c) 1998 -- University of Notre Dame -- -- Permission to use, copy, modify, distribute and sell this software -- and its documentation for any purpose is hereby granted without fee, -- provided that the above copyright notice appears in all copies and -- that both that copyright notice and this permission notice appear -- in supporting documentation. The University of Notre Dame makes no -- representations about the suitability of this software for any -- purpose. It is provided "as is" without express or implied warranty. -- --><HEAD><TITLE>Description of sin</TITLE></HEAD><BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" ALINK="#ff0000"> <FONT FACE=Helvetica><!--end header--><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=2 WIDTH=100%><TR><TD><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=100%><TR><TD Align=left valign=middle width=440 rowspan=2><FONT FACE=verdana,arial,helvetica SIZE=+3 COLOR=#110088><B>sin</B></FONT></TD><TD valign=middle Align=right width=128 rowspan=2><A HREF="http://lsc.nd.edu/research/mtl"><IMG BORDER=0 SRC="./glossy-mtl-logo.jpg" height=48 ALT="[MTL Home]"></A></TD><TD Align=center width=280 nowrap><Font face=verdana,arial,helvetica size=+3><b>Programmers Guide</b></font></TD></TR><TR BGCOLOR='#2020b0'><TD HEIGHT=20 VALIGN='MIDDLE' NOWRAP align=center STYLE="font-family:verdana,arial,helvetica;font-weight:bold;"> <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./table_of_contents.html">Contents</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./mtl_index.html">Index</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="http://lsc.nd.edu/research/mtl/search.html">Search</A> </TD></TR></TABLE></TD></TR><TR><TD><Table CellPadding=0 CellSpacing=0 width=100% cols=2><TR><TD Align=left><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "intervals.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR><TR><TD><Img src = "math.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD><TD Align=right><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "function.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD></TR><TR><TD Align=left VAlign=top><b>Category</b>:intervals,math</TD><TD Align=right VAlign=top><b>Component type</b>:function</TD></TR></Table></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Prototype</B></FONT></TD></TR><TR><TD><TT>template <class Tnum><br> <A HREF="interval.html" >interval</A><Tnum> <B>sin</B>(const <A HREF="interval.html" >interval</A><Tnum>& x) ;</TT></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Description</B></FONT></TD></TR><TR><TD>Computes the trigonometric sine of an <A HREF="interval.html" >interval</A>. If the <A HREF="interval.html" >interval</A>'sleft bound is not less than 0 or if its right bound is greater than 2*pi, then it will print <br><code>bad argument for restricted sine of [<B>x</B>,<B>y</B>]</code> <br>where <b>x</b> and <b>y</b> are the bounds of the <A HREF="interval.html" >interval</A> and will return NaN.<pre> distance_left = right(x) - piby2() distance_right = piby2() - left(x) sin(x) = if (piby2 & x) != empty: [-1.0,1.0] if sup(x & pi3by2) != 0 and inf(x & pi3by2) != 0 [sin(sup(x),1.0] if inf(distance_right) > sup(distance_left) [sin(inf(x),1.0] else if inf(distance_left) > sup(distance_right) [sin(sup(x),1.0] else if sin(inf(x)) > sin(sup(x)) [sin(inf(x),1.0] else if (pi3by2 & x) != empty: [-1.0,sin(sup(x))] if inf(distance_right) > sup(distance_left) [-1.0,sin(inf(x))] if inf(distance_left) > sup(distance_right) [-1.0,sin(sup(x))] else if sin(sup(x)) > sin(left(x)) [-1.0,sin(inf(x))] else if sup(x) < inf(piby2) or inf(x) > sup(pi3by2): [sin(inf(x)),sin(sup(x))] else: [sin(sup(x)),sin(inf(x))]</pre></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Definition</B></FONT></TD></TR><TR><TD><A HREF="../../../contrib/interval/interval.cct">interval.cct</A></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Preconditions</B></FONT></TD></TR><TR><TD><UL></UL></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Complexity</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Example</B></FONT></TD></TR><TR><TD>In <A HREF=file:/afs/nd.edu/user1/lsc/Students/arodrig6/MTL-learn/mtl2/mtl/contrib/interval/doc/expamples/mathfunc.cc>mathfunc.cc</A>:<PRE> cout << "A:" << A << endl << endl; cout << "Square :" << sqr(A) << endl; cout << "Square Root:" << sqrt(A) << endl; cout << "Tangent :" << tan(A) << endl; cout << "ArcTangent :" << atan(A) << endl; cout << "Sine :" << sin(A) << endl; cout << "Cosine :" << cos(A) << endl; cout << "Arcsine :" << asin(A) << endl; cout << "Arcosine :" << acos(A) << endl; cout << "Log :" << log(A) << endl; cout << "Ln :" << ln(A) << endl; cout << "Power (A^A):" << pow(A,A) << endl; cout << "Exponent :" << exp(A) << endl;</PRE></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Notes</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>See also</B></FONT></TD></TR><TR><TD></TD></TR></TABLE><!--start footer--> <P><CENTER><CENTER><IMG SRC="./blue-bar.jpg" width=640></CENTER></CENTER><P><A HREF="http://www.nd.edu"><IMG BORDER=0 SRC="./ndtoclogo.gif" ALT="[MTL Home]" ALIGN=absmiddle></A></A><FONT SIZE="-2"><A HREF="../LICENSE.htm">Copyright ©1998,1999 University of Notre Dame. 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