document.write( "Question 1063200: I need to solve this equation for 0 < x< 2pi
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Algebra.Com's Answer #678274 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "I need to solve this equation for 0 < x < 2pi
\n" ); document.write( " -2tan(-2x + 4pi/3) = 2sqrt3
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document.write( "\"+-2tan%28-2x+%2B+4pi%2F3%29\" = \"2%2Asqrt%283%29\"  ----->  (divide both sides by (-2) )  --->\r\n" );
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document.write( "\"tan%28-2x%2B+4pi%2F3%29\" = \"-sqrt%283%29\"  ---->  \r\n" );
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document.write( "The last equation has solutions  \"-2x+%2B+4pi%2F3\" = \"2pi%2F3+%2B+k%2Api\", k = 0, +/-1, +/-2, , , , .\r\n" );
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document.write( "Let's derive an expression for x from this:\r\n" );
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document.write( "\"-2x+%2B+4pi%2F3\" = \"2pi%2F3+%2B+k%2Api\"   ---->  \"2%2A%28-x+%2B+2pi%2F3%29\" = \"2pi%2F3+%2B+k%2Api\"  ---->  \"-x+%2B+2pi%2F3\" = \"pi%2F3+%2B+k%2A%28pi%2F2%29\"  ---->  x = \"pi%2F3+%2B+k%2A%28pi%2F2%29\", k = 0, +/-1, +/-2, , , , .\r\n" );
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document.write( "In the given interval (\"0\",\"2%2Api\") \r\n" );
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document.write( "x = \"pi%2F3\", \"pi%2F3+%2B+pi%2F2\", \"pi%2F3%2Bpi\", \"pi%2F3%2B+3pi%2F2\" are the solutions.\r\n" );
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document.write( "Answer. In the given interval the solutions are   = \"pi%2F3\", \"5pi%2F6\", \"4pi%2F3\", \"11pi%2F6\".    (See the plot below)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Plots y = \"-2tan%28-2x+%2B+4pi%2F3%29\" and y = \"2%2Asqrt%283%29\"\r
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\n" ); document.write( "\n" ); document.write( "To see more examples of solved trigonometry equations with detailed solutions, 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( "    - Proving Trigonometry identities\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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