document.write( "Question 1042988: How can i solve these trigonometric functions?\r
\n" ); document.write( "\n" ); document.write( " Solve for x∈[0,2π]:
\n" ); document.write( "\"+sin%283x%29=-1%2Fsqrt%282%29+\"\r
\n" ); document.write( "\n" ); document.write( "also if you've got time\r
\n" ); document.write( "\n" ); document.write( "Solve for x∈[0,2π]:
\n" ); document.write( "\"+sin%282x%29=-1%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "I don't get how my answers are wrong after i solve it..\r
\n" ); document.write( "\n" ); document.write( "Thanks!! \n" ); document.write( "
Algebra.Com's Answer #658073 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
The good lady did not get all the solutions\r\n" );
document.write( "between 0 and \"2pi\".  There are 6 solutions for\r\n" );
document.write( "the first one and 4 solutions for the second one.\r\n" );
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\n" ); document.write( "How can i solve these trigonometric functions?
\n" ); document.write( "Solve for x∈[0,2π]:
\n" ); document.write( "\"sin%283x%29=-1%2Fsqrt%282%29\"
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document.write( "The sine is negative in QIII and QIV\r\n" );
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document.write( "Rationalize the denominator of \"-1%2Fsqrt%282%29\"\r\n" );
document.write( "and get \"-sqrt%282%29%2F2\" and from your knowledge\r\n" );
document.write( "of special angles or from the unit circle,\r\n" );
document.write( "the solutions for 3x are 225° and 315° or\r\n" );
document.write( "since you are using radians, \"5pi%2F4\" and \"7pi%2F4\".\r\n" );
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document.write( "However, the left side is sin(3x), not sin(x).\r\n" );
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document.write( "That means we must get 3 times as many answers for x\r\n" );
document.write( "as we would get for 3x.\r\n" );
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document.write( "To do that we add \"2pi\" 3-1 = 2 times to each of those\r\n" );
document.write( "answers for 3x in order to get all non-negative answers for \r\n" );
document.write( "x less than \"2pi\":\r\n" );
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document.write( "So \r\n" );
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document.write( "1.  we have to add \"2pi\" and \"4pi\" to the first answer\"5pi%2F4\":  \r\n" );
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document.write( "which we get LCDs and simplify as\r\n" );
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document.write( "and simplify further as\r\n" );
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document.write( "Then divide through by 3 (multiply through by \"1%2F3\" and get:\r\n" );
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document.write( "or\r\n" );
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document.write( "Also,\r\n" );
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document.write( "2.  we have to add \"2pi\" and \"4pi\" to the second answer\"7pi%2F4\":  \r\n" );
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document.write( "We get the LCD:\r\n" );
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document.write( "and simplify further as\r\n" );
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document.write( "\r\n" );
document.write( "Then divide through by 3 (multiply through by \"1%2F3\") and get:\r\n" );
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document.write( "or\r\n" );
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document.write( "All the 6 solutions in order of magnitude are\r\n" );
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document.write( "------------------------\r\n" );
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document.write( "Solve for x∈[0,2π]:\r\n" );
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document.write( "\"sin%282x%29=-1%2F2\"\r\n" );
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document.write( "As before, the sine is negative in QIII and QIV.\r\n" );
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document.write( "From your knowledge of special angles or from the unit \r\n" );
document.write( "circle, the solutions for sin(2x) are 210° and 330° or\r\n" );
document.write( "since you are using radians, \"7pi%2F6\" and \"11pi%2F6\".\r\n" );
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document.write( "However, the left side is sin(2x), not sin(x).\r\n" );
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document.write( "That means we must get 2 times as many answers for x\r\n" );
document.write( "as we would get for 2x.\r\n" );
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document.write( "To do that we add \"2pi\" 2-1 = 1 time to each of those\r\n" );
document.write( "answers for 2x in order to get all non-negative answers for \r\n" );
document.write( "x less than \"2pi\":\r\n" );
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document.write( "So \r\n" );
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document.write( "1.  we have to add \"2pi\" to the first answer\"7pi%2F6\":  \r\n" );
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document.write( "We get the LCD:\r\n" );
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document.write( "and simplify further as\r\n" );
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document.write( "\"matrix%281%2C7%2C2x%2C%22%22%2C%22%22=%22%22%2C%22%22%2C7pi%2F6%2C%22%2C%22%2C19pi%2F6%29\"\r\n" );
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document.write( "Then divide through by 2 (multiply through by \"1%2F2\") and get:\r\n" );
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document.write( "or\r\n" );
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document.write( "\"matrix%281%2C7%2Cx%2C%22%22%2C%22%22=%22%22%2C%22%22%2C7pi%2F12%2C%22%2C%22%2C19pi%2F12%29\"\r\n" );
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document.write( "Also,\r\n" );
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document.write( "2.  we have to add \"2pi\" to the second answer \"11pi%2F6\":  \r\n" );
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document.write( "which we get LCDs and simplify as\r\n" );
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document.write( "and simplify further as\r\n" );
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document.write( "\"matrix%281%2C7%2C2x%2C%22%22%2C%22%22=%22%22%2C%22%22%2C11pi%2F6%2C%22%2C%22%2C23pi%2F6%29\"\r\n" );
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document.write( "Then divide through by 2 (multiply through by \"1%2F2\" and get:\r\n" );
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document.write( "or\r\n" );
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document.write( "\"matrix%281%2C7%2Cx%2C%22%22%2C%22%22=%22%22%2C%22%22%2C11pi%2F12%2C%22%2C%22%2C23pi%2F12%29\"\r\n" );
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document.write( "All the 4 solutions in order of magnitude are\r\n" );
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document.write( "Edwin
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