document.write( "Question 1036835: Write polar equation in rectangular form.
\n" ); document.write( "r=6sin(theta) \n" ); document.write( "
Algebra.Com's Answer #651645 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"r\"\"%22%22=%22%22\"\"6sin%28theta%29\"\r\n" );
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document.write( "If we draw the graph of that on polar graph paper. we make\r\n" );
document.write( "a table of points:\r\n" );
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document.write( "  q | r\r\n" );
document.write( "  0院0.00\r\n" );
document.write( " 15院1.55\r\n" );
document.write( " 30院3.00\r\n" );
document.write( " 45院4.24\r\n" );
document.write( " 60院5.20\r\n" );
document.write( " 75院5.80\r\n" );
document.write( " 90院6.00\r\n" );
document.write( "105院5.80\r\n" );
document.write( "120院5.20\r\n" );
document.write( "135院4.24\r\n" );
document.write( "150院3.00\r\n" );
document.write( "165院1.55\r\n" );
document.write( "180院0.00\r\n" );
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document.write( "We get this circle:\r\n" );
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document.write( "When changing from one form to the other always draw this first:\r\n" );
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document.write( "We substitute for the sine first.\r\n" );
document.write( "Looking at the triangle and remembering that\r\n" );
document.write( "\"SINE=OPPOSITE%2FHYPOTENUSE\" \r\n" );
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document.write( "\"sin%28theta%29=y%2Fr\"\r\n" );
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document.write( "so substitute \"y%2Fr\" for \"sin%28theta%29\" first\r\n" );
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document.write( "\"r\"\"%22%22=%22%22\"\"6%28y%2Fr%29\"\r\n" );
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document.write( "\"r\"\"%22%22=%22%22\"\"%286y%29%2Fr\"\r\n" );
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document.write( "Multiply both sides by r\r\n" );
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document.write( "\"r%5E2\"\"%22%22=%22%22\"\"6y\"\r\n" );
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document.write( "Now use the Pythagorean theorem to substitute \"x%5E2%2By%5E2\"\r\n" );
document.write( "for \"r%5E2\"\r\n" );
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document.write( "\"x%5E2%2By%5E2\"\"%22%22=%22%22\"\"6y\"  <-- answer\r\n" );
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document.write( "As a check let's graph it.\r\n" );
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document.write( "Get it in standard form:\r\n" );
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document.write( "\"x%5E2%2By%5E2-6y\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Write x as (x-0)\r\n" );
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document.write( "Complethe square:\r\n" );
document.write( "take half or -6, get -3\r\n" );
document.write( "Square it, get 9\r\n" );
document.write( "Add 9 to both sides:\r\n" );
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document.write( "\"%28x-0%29%5E2%2By%5E2-6y%2B9\"\"%22%22=%22%22\"\"9\"\r\n" );
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document.write( "Factor the trinomial in y:\r\n" );
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document.write( "\"%28x-0%29%5E2%2B%28y-3%29%5E2\"\"%22%22=%22%22\"\"9\"\r\n" );
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document.write( "That's a circle with center (0,3) and radius 3:\r\n" );
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document.write( "It graphs as the same circle, so we are right.\r\n" );
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document.write( "Edwin
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