document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026502>Question 1026502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following equation for theta, 0 < theta < 360, rounded to the nereast tenth of a degree.\r<BR>\n" );
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document.write( "2cos theta=5+6/cos theta\r<BR>\n" );
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document.write( "1.{27.6°}<BR>\n" );
document.write( "2.{27.6°, 332.4°}<BR>\n" );
document.write( "3.{152.4°, 207.6°}<BR>\n" );
document.write( "4. 2 and 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641806 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=641806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> answer is selection 3.\r<BR>\n" );
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document.write( "here's why.\r<BR>\n" );
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document.write( "start with 2 * cos(theta) = 5 + (6 / cos(theta) \r<BR>\n" );
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document.write( "multiply both sides of the equation by cos(theta) to get:\r<BR>\n" );
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document.write( "2 * cos^2(theta) = 5 * cos(theta) + 6\r<BR>\n" );
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document.write( "subtract the right side of the equation from both sides of the equation to get:\r<BR>\n" );
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document.write( "2 * cos^2(theta) - 5 * cos(theta) - 6 = 0.\r<BR>\n" );
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document.write( "this is a quadratic equation.\r<BR>\n" );
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document.write( "solve it using the quadratic formula.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "cos(theta) = -.8860009 or cos(theta) = 3.3860009\r<BR>\n" );
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document.write( "since cos(theta) has to be less than 1 or greater than -1, cos(theta) = 3.3860009 is not valid.\r<BR>\n" );
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document.write( "the only solution is cos(theta) = -.8860009.\r<BR>\n" );
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document.write( "the cosine function is negative in quadrants 2 and 3.\r<BR>\n" );
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document.write( "it is positive in quadrants 1 and 4.\r<BR>\n" );
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document.write( "to find the equivalent angle in quadrant 1, make the cosine positive.\r<BR>\n" );
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document.write( "you will get cos(theta) = .8860009.\r<BR>\n" );
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document.write( "solve for theta to get theta = arccos(.8860009) = 27.6250548 degrees.\r<BR>\n" );
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document.write( "the equivalent angle in the second quadrant is 180 degrees minus that.\r<BR>\n" );
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document.write( "the equivalent angle in the third quadrant is 180 degrees plus that.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "theta = 152.3749452 in the second quadrant and theta = 207.6250548 in the third quadrant.\r<BR>\n" );
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document.write( "round to nearest tenth of a degrees and you get:\r<BR>\n" );
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document.write( "theta = 152.4 in the second quadrant and theta = 207.6 in the third quadrant.\r<BR>\n" );
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document.write( "that agrees with selection 3.\r<BR>\n" );
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document.write( "find cos(152.4) with your calculator and you will see that it is equal to -.886.....\r<BR>\n" );
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document.write( "find cos(207.6) with your calculator and you will see that it is equal to -.886... as well.\r<BR>\n" );
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document.write( "the calculator confirms that the angles are correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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