document.write( "Question 1064475: If $\"cos%28theta%29+=+sqrt%28+1%2F2+%2B+1%2F%282+%2A+sqrt%28+2+%29%29%29+\"$ and $\"sin%28theta%29+=+sqrt%28+1%2F2+-+1%2F%282+%2A+sqrt%28+2+%29%29%29+\"$ with $\"0+%3C=+theta+%3C+2pi\"$ it follows that $\"2theta\"$ = .... $\"pi\"$ \r
\n" ); document.write( "\n" ); document.write( "the answer is $\"15pi+%2F+4\"$ but I got only $\"7pi%2F4\"$ What did I do wrong? \n" ); document.write( "

Algebra.Com's Answer #679514 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "If $\"cos%28theta%29+=+sqrt%28+1%2F2+%2B+1%2F%282+%2A+sqrt%28+2+%29%29%29+\"$ and $\"sin%28theta%29+=+sqrt%28+1%2F2+-+1%2F%282+%2A+sqrt%28+2+%29%29%29+\"$ with $\"0+%3C=+theta+%3C+2pi\"$ it follows that $\"2theta\"$ = .... $\"pi\"$ \r
\n" ); document.write( "\n" ); document.write( "the answer is $\"15pi+%2F+4\"$ but I got only $\"7pi%2F4\"$ What did I do wrong?
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document.write( "You correctly determined that  = .\r\n" );
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document.write( "Notice that both  and  are positive, as it is (implicitly) stated by the condition.\r\n" );
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document.write( "Hence,  lies in QI.\r\n" );
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document.write( "Therefore  can be one of the two angles:  or  and CAN NOT be anything different.\r\n" );
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document.write( "Moreover, since   < , the angle  is less than .\r\n" );
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document.write( "Therefore,  =  and CAN NOT be anything different.\r\n" );
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