document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151647>Question 1151647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if cos x°= sin 200° , find the possible values of X between -180° and 360°<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773460 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=773460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cos(x) = sin(200)<BR>\n" );
document.write( "this means that x = arccos(sin(200))<BR>\n" );
document.write( "solve for x to get x = 110 degrees.<BR>\n" );
document.write( "that's in the second quadrant.<BR>\n" );
document.write( "solve for sin(200) to get sin(200) = -.3420201433.<BR>\n" );
document.write( "this is negative.<BR>\n" );
document.write( "since cos(x) equals this, then cosine is negative.<BR>\n" );
document.write( "that would be in the second and third quadrants only.<BR>\n" );
document.write( "the equivalent angle in the first quadrant is 180 - 110 = 70 degrees.<BR>\n" );
document.write( "the equivalent angle in the third quadrant is 180 + 70 = 250 degrees.<BR>\n" );
document.write( "so far you have 110 degrees and 250 degrees.<BR>\n" );
document.write( "subtract 360 from these to get equivalent angles of -250 degrees and minus 110 degrees.<BR>\n" );
document.write( "since you want angles between -180 and 360 degrees, your solution will be that x = -110 degrees, 110 degrees, and 250 degrees.<BR>\n" );
document.write( "to confirm, i graphed the equation of y = cos(x) and y = sin(200).<BR>\n" );
document.write( "you can see from this graph that y = arccos(sin(200)) occurs at -180, 110, and 250 degrees when you go between -180 degrees and 360 degrees.\r<BR>\n" );
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document.write( "note that y = arccos(sin(200)) is the same as y = arccos(-.342) as shown on the graph.<BR>\n" );
document.write( "-.342 shown on the graph is really -.3420201433 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "first graph is the equations used.<BR>\n" );
document.write( "second graph is the graph of the equations used.\r<BR>\n" );
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