document.write( "Question 1039861: Find PARAMETRIC EQUATIONS for the path of a particle that moves clockwise twice around the circle (x-3)^2+y^2=16, starting from (-1,0). \n" ); document.write( "

Algebra.Com's Answer #654726 by robertb(5830) $\"\"$ $\"About$

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Suppose first that the parametrization goes only once around the circle for [0, $\"2%2Api\"$ ].\r
\n" ); document.write( "\n" ); document.write( "Then you can use the parametrization\r
\n" ); document.write( "\n" ); document.write( " $\"x+-+3+=+4cos%28pi-t%29\"$ and $\"y=+4sin%28pi-t%29\"$ ,\r
\n" ); document.write( "\n" ); document.write( "or, which is the same thing (after doing a little trigonometry), \r
\n" ); document.write( "\n" ); document.write( " $\"x+-+3+=+-4cost\"$ and $\"y=+4sint\"$ .\r
\n" ); document.write( "\n" ); document.write( "Since we want two rotations for t in [0, $\"2%2Api\"$ ], just let\r
\n" ); document.write( "\n" ); document.write( " $\"x+-+3+=+-4cos2t\"$ and $\"y=+4sin2t\"$ , or \r
\n" ); document.write( "\n" ); document.write( " $\"x+=3+-4cos2t\"$ and $\"y=+4sin2t\"$ \n" ); document.write( "

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