document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956325>Question 956325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Algebraically determine the solution to the following equations. Provide answers that are appropriate taking into consideration the stated domains.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+cos+theta+-2=-3+ ALIGN=MIDDLE  ALT=\"+7+cos+theta+-2=-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > over the domain, -180 degrees <(or equal to) x <(or equal to) 180 degrees </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584250 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=584250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 7 * cos(theta) - 2 = -3<BR>\n" );
document.write( "add 2 to both sides of the equation to get:<BR>\n" );
document.write( "7 * cos(theta) = -1<BR>\n" );
document.write( "divide both sides of the equation by 7 to get:<BR>\n" );
document.write( "cos(theta) = -1/7\r<BR>\n" );
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document.write( "to find the reference angle, make cos(theta) = positive.\r<BR>\n" );
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document.write( "you will get cos(theta) = 1/7\r<BR>\n" );
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document.write( "use your calculator to solve for theta to get:\r<BR>\n" );
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document.write( "theta = arccos(1/7) = 81.7867893 degrees.\r<BR>\n" );
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document.write( "since cos(theta) needs to be negative, then your angle has to be in quadrant 2 or quadrant 3.\r<BR>\n" );
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document.write( "your angle in quadrant 2 is equal to 180 - 81.7867893 which is equal to 98.2132107 degrees.\r<BR>\n" );
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document.write( "your angle in quadrant 3 is equal to 180 + 81.7867893 which is equal to 261.7867893 degrees.\r<BR>\n" );
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document.write( "your interval is from -180 to 180.\r<BR>\n" );
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document.write( "261.7867893 degrees doesn't work because it is greater than 180.\r<BR>\n" );
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document.write( "since trig functions are repetitive, then your solution is actually:\r<BR>\n" );
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document.write( "98.2132107 plus or minus k * 360, where k is a non-negative integer, ....\r<BR>\n" );
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document.write( "and 261.7867893 plus or minus k * 360, where k is a non-negative integer.\r<BR>\n" );
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document.write( "98.2132107 is within your domain of -180 to 180, so that solution is good.\r<BR>\n" );
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document.write( "261.7867893 - 1 * 360 is equal to -98.2132107 which is also within your domain, so that solution is also good.\r<BR>\n" );
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document.write( "none of the other solutions are within your domain, so those two solutions are the only valid solutions that are within the required domain interval.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "theta = 98.2132107 degrees and theta = -98.2132107 degrees.\r<BR>\n" );
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document.write( "a graph of your equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/031701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "this graph shows both equations separately.\r<BR>\n" );
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document.write( "the solution is the intersection of the graphs of the two equations.\r<BR>\n" );
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document.write( "first equation is y = 7 * cos(theta) - 2\r<BR>\n" );
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document.write( "second equation is y = -3\r<BR>\n" );
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document.write( "the intersection of the two graphs is when y = 7 * cos(theta) - 1 is equal to y = -3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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