document.write( "Question 1088061: Find all solutions in the interval [0,360)
\n" ); document.write( "cos^2(theta)+8cos(theta)+5=0 \n" ); document.write( "
Algebra.Com's Answer #702334 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "Find all solutions in the interval [0,360)
\n" ); document.write( "cos^2(theta)+8cos(theta)+5=0
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document.write( "\"cos%5E2%28theta%29+%2B+8cos%28theta%29+%2B+5\" = 0.\r\n" );
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document.write( "Introduce new variable x = \"cos%28theta%29\". Then your equation takes the form\r\n" );
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document.write( "\"x%5E2+%2B+8x+%2B+5\" = 0.\r\n" );
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document.write( "Apply the quadratic formula to solve for x:\r\n" );
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document.write( "\"x%5B1%2C2%5D\" = \"%28-8+%2B-+sqrt%288%5E2+-+4%2A1%2A5%29%29%2F2\" = \"%28-8+%2B-+sqrt%2844%29%29%2F2\" = \"-4+%2B-+sqrt%2811%29\".\r\n" );
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document.write( "1)  \"x%5B1%5D\" = \"-4+%2B+sqrt%2811%29%29\" =~ -0.68.\r\n" );
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document.write( "    \"cos%28theta%29\" = \"-4+%2B+sqrt%2811%29\"  ====>  \"theta\" = \"arccos%28-4+%2B+sqrt%2811%29%29\"  and  \"theta\" = \"2pi+-+arccos%28-4+%2B+sqrt%2811%29%29\".\r\n" );
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document.write( "2)  \"x%5B2%5D\" = \"-4+-+sqrt%2811%29%29\" < -1.\r\n" );
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document.write( "    There is NO \"theta\" satisfying \"cos%28theta%29\" = \"x%5B2%5D\".\r\n" );
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document.write( "Answer. The original equation has two solutions  \"theta\" = \"arccos%28-4+%2B+sqrt%2811%29%29\"  and  \"theta\" = \"2pi+-+arccos%28-4+%2B+sqrt%2811%29%29\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see more solved problems/samples on trigonometric equations, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving simple problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving advanced problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on calculating trig functions and solving trig equations\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Trigonometry: Solved problems\". \r
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