document.write( "Question 1208069: what is the possible values of x in 2sin^2(x-30)=cos 60
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Algebra.Com's Answer #846211 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "what $\"highlight%28cross%28is%29%29\"$ are the possible values of x in 2sin^2(x-30)=cos 60
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document.write( "They want you find all real solutions to this equation\r\n" );
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document.write( "    2sin^2(x-30) = cos(60).    (1)\r\n" );
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document.write( "We have \r\n" );
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document.write( "    cos(60) = 1/2;  so, this equation takes the form\r\n" );
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document.write( "    2sin^2(x-30) = 1/2.\r\n" );
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document.write( "Simplify it step by step\r\n" );
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document.write( "    sin^2(x-30) = 1/4,\r\n" );
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document.write( "    sin(x-30) = +/-},\r\n" );
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document.write( "    sin(x-30) = +/- 1/2.    (2)\r\n" );
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document.write( "From this equation, there are two infinite sets of roots for  x-30  to equation  (2)\r\n" );
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document.write( "    x-30 = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "    x-30 = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "It gives two infinite sets of roots for  x  to equation  (1)\r\n" );
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document.write( "    x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "    x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "ANSWER.  Equation (1) has two infinite sets of solutions\r\n" );
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document.write( "             x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "             x = ,  k = 0, +/-1, +/-2, . . . \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "To tutor @greenestamps and to all other readers of this post.\r
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\n" ); document.write( "\n" ); document.write( "        Thank you for your attention, but my solution, as it is/was written by me \r
\n" ); document.write( "\n" ); document.write( "        from the very beginning, is correct and includes all the cases   sin(x-30) = +/- 1/2.\r
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\n" ); document.write( "\n" ); document.write( "        It is because the general formula uses not full period $\"2pi\"$ , but half period $\"pi\"$ , which absorbs/covers all these cases.\r
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\n" ); document.write( "\n" ); document.write( "        So, everything is and was correct in my post.   There is no reason to worry.\r
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\n" ); document.write( "\n" ); document.write( "        This alarm from @greenestamps is false.\r
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