document.write( "Question 1206160: Solve for (0<=x<=360)
\n" ); document.write( "sin2x-cosx=-1+2sinx
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Algebra.Com's Answer #843431 by ikleyn(52814)\"\" \"About 
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document.write( "          Step by step\r\n" );
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document.write( "sin(2x) - cos(x) = -1 + 2sin(x)\r\n" );
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document.write( "2sin(x)cos(x) - cos(x) = -1 + 2sin(x)\r\n" );
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document.write( "cos(x)*(2sin(x) - 1) = -1 + 2sin(x)\r\n" );
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document.write( "cos(x)*(2sin(x) - 1) - (-1 + 2sin(x)) = 0\r\n" );
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document.write( "(cos(x)-1)*(2sin(x)-1) = 0\r\n" );
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document.write( "Case 1:  cos(x)-1 = 0    --->  cos(x) = 1  --->  x = 0.\r\n" );
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document.write( "Case 2:  2sin(x) -1 = 0  --->  2sin(x) = 1  --->  sin(x) = 1/2  --->  x = 30 degrees or x = 150 degrees.\r\n" );
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document.write( "ANSWER.  There are 3 (three) solutions: x= 0 degrees;  x = 30 degrees and x= 150 degrees.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For this problem, and for many other problems,  if the restriction for the argument\r
\n" ); document.write( "\n" ); document.write( "is for one period,  it is usually  (ALWAYS)  should be written in the form   0 <= x < 360
\n" ); document.write( "and  NOT  in the form   0 <= x <= 360,  because  0  and  360  represents
\n" ); document.write( "the same geometric angle  (although different numbers).\r
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\n" ); document.write( "\n" ); document.write( "This small detail - how do you write this restriction - in correct form   0 <= x < 360\r
\n" ); document.write( "\n" ); document.write( "or in incorrect form  0 <= x <= 360,  makes it clear from the first glance\r
\n" ); document.write( "\n" ); document.write( "whether you know the subject and are familiar with standard mathematical notations - or not.\r
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