document.write( "Question 678713: How to find the rectangular coordinates, when given the polar coordinates?
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Algebra.Com's Answer #421672 by Edwin McCravy(20063) $\"\"$ $\"About$

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How to find the rectangular coordinates, when given the polar coordinates?
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document.write( "The formula to convert \r\n" );
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document.write( "Polar point (r,) to the rectangular point (x,y) is given by\r\n" );
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document.write( "x = r·cos(), y = r·cos().\r\n" );
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document.write( "Here r = -4 and  = 4 radians. Substituting, we have:\r\n" );
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document.write( "x = -4·cos(4) = 2.614574483, y = -4·cos(4) = 3.027209981\r\n" );
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document.write( "So the answer is:\r\n" );
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document.write( "the rectangular point (x,y) = (2.614574483, 3.027209981),\r\n" );
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document.write( "or rounded to hundredths, (2.61,3.03).\r\n" );
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document.write( "Let's show how that works: \r\n" );
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document.write( "When r is positive the point will be in the same quadrant as θ.\r\n" );
document.write( "On the other hand when r is negative the point will end up in the \r\n" );
document.write( "quadrant exactly opposite θ.    \r\n" );
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document.write( "The angle , the second polar coordinate, is 4 radians.  \r\n" );
document.write( "Converting that to degrees gives us  = 229.1831181°,\r\n" );
document.write( "which is between 180° and 270°. which means it is an angle in the \r\n" );
document.write( "3rd quadrant.\r\n" );
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document.write( "Let's first plot the polar point (4,4).  Then we'll reflect it through\r\n" );
document.write( "the origin to the quadrant opposite 4 radians, which will be the 1st\r\n" );
document.write( "quadrant.        \r\n" );
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document.write( "We swing a radius 4 units long through an arc counter-clockwise from\r\n" );
document.write( "the right side of the x-axis 229.1831181° around to the 3rd quadrant,\r\n" );
document.write( "like this:\r\n" );
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document.write( "The point (4,4) is marked with a small circle.  However we want the \r\n" );
document.write( "point (-4,4), not (4,4), so we reflect it through the origin to the\r\n" );
document.write( "quadrant opposite the 3rd quadrant, which is the 1st quadrant, like\r\n" );
document.write( "this:\r\n" );
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document.write( "That polar point (-4,4) is the same point as this rectangular point\r\n" );
document.write( "(2.61, 3.03):\r\n" );
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document.write( "Edwin

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