document.write( "Question 1058119: How do I solve the equation the equation sin(theta) - cos(theta) = sqrt( 2 ) ? \n" ); document.write( "

Algebra.Com's Answer #673155 by ikleyn(52852) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "How do I solve the equation the equation sin(theta) - cos(theta) = sqrt( 2 ) ?
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document.write( " = .\r\n" );
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document.write( "Multiply both sides by . You will get\r\n" );
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document.write( " = 1.             (1)\r\n" );
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document.write( "Notice and use that  =  = .\r\n" );
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document.write( "Then from (*) you will get \r\n" );
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document.write( " = 1.       (2)\r\n" );
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document.write( "Now use the formula sin(a)*cos(b) - cos(a)*sin(b) = sin(a-b). Then from (2) you will get\r\n" );
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document.write( " = 1.\r\n" );
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document.write( "It implies \r\n" );
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document.write( " = .\r\n" );
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document.write( "Then  =  = .\r\n" );
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document.write( "It is the same as  =  in the interval 0 <=  < .\r\n" );
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\n" ); document.write( "\n" ); document.write( "The plot below confirms the solution ( $\"3pi%2F4\"$ ~= 2.33 )\r
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\n" ); document.write( "\n" ); document.write( "Plots y = $\"sin%28theta%29+-+cos%28theta%29\"$ and y = $\"sqrt%282%29\"$ \r
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\n" ); document.write( "There is a bunch of my lessons on solving trig equations in this site \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( "    - OVERVIEW of lessons on calculating trig functions and solving trig equations\r
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