document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116912>Question 1116912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find x where 0<\x<\360\r<BR>\n" );
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document.write( "A) sec x + 4cos x =5\r<BR>\n" );
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document.write( "Plz help me i try lots but invain.<BR>\n" );
document.write( "thx in adv </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731830 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=731830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is sec(x) + 4cos(x) = 5\r<BR>\n" );
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document.write( "sec(x) is equivalent to 1/cos(x).\r<BR>\n" );
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document.write( "your equation becomes 1/cos(x) + 4cos(x) = 5\r<BR>\n" );
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document.write( "multiply both sides of the equation by cos(x) to get:\r<BR>\n" );
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document.write( "1 + 4cos^2(x) = 5cos(x)\r<BR>\n" );
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document.write( "subtract 5cos(x) from both sides of the equation to get 1 + 4cos^2(x) - 5cos(x) = 0\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "4cos^2(x) - 5cos(x) + 1 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "cos(x) = .25 or cos(x) = 1\r<BR>\n" );
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document.write( "in the first quadrant, cos(x) = 1 when x = 0 degrees.\r<BR>\n" );
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document.write( "in the first quadrant, cos(x) = .25 when x = 75.52248781.\r<BR>\n" );
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document.write( "cos(x) is positive in the first and fourth quadrant.\r<BR>\n" );
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document.write( "in the fourth quadrant, 0 degrees is equal to 360 - 0 = 360 degrees.\r<BR>\n" );
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document.write( "in the fourth quadrant, 75.52248781 degrees is equal to 360 - 75.52248781 = 284.4775122 degrees.\r<BR>\n" );
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document.write( "your solution is that:\r<BR>\n" );
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document.write( "x = 0, 75.52248781, 284.4775122, 360 degrees in the interval from 0 to 360 degrees.\r<BR>\n" );
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document.write( "that would be the interval 0 <= x <= 360 degrees.\r<BR>\n" );
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document.write( "in the interval 0 < x < 360 degrees, then your only solutions are x = 75.52248781 or x = 284.4775122.\r<BR>\n" );
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document.write( "here's a graph of your equation with the possible solutions shown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/051001.jpg\" alt=\"$$$\" > </SPAN>\n" );
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