document.write( "Question 828733: Convert each point from the given cartesian coordinates to polar coordinates. Find polar coordinates with -pi/2 < theta <= pi/2. \r
\n" ); document.write( "\n" ); document.write( "a) If (x, y) = (20,-4) then (r, theta)=\r
\n" ); document.write( "\n" ); document.write( "b) If (x, y) = (1,2) then (r, theta)=\r
\n" ); document.write( "\n" ); document.write( "c) If (x, y) = (-2,1) then (r, theta)=\r
\n" ); document.write( "\n" ); document.write( "d) If (x, y) = (16,6) then (r, theta)=\r
\n" ); document.write( "\n" ); document.write( "e) If (x, y) = (-7,-8) then (r, theta)=\r
\n" ); document.write( "\n" ); document.write( "f) If (x, y) = (0,-4) then (r, theta)= \n" ); document.write( "
Algebra.Com's Answer #499528 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "a) If (x, y) = (20,-4) then (r, theta)= \r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "We use these conversions to translate from Cartesian to Polar Coordinates. Note the quadrant \r\n" );
document.write( "in which (x,y) lies in order to select the correct angle (between -pi/2 and pi/2).\r\n" );
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document.write( "r = sqrt(x^2 + y^2)\r\n" );
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document.write( "where\r\n" );
document.write( "r is distance from origin to the point\r\n" );
document.write( "x is value of the x-coordinate\r\n" );
document.write( "y is value of the y-coordinate\r\n" );
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document.write( " θ = arctan(y/x)  \r\n" );
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document.write( "where\r\n" );
document.write( "θ = angle relative to the zero axis (in degrees)\r\n" );
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document.write( "Given (x, y) = (20,-4) then\r\n" );
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document.write( "r = sqrt(x^2 + y^2)\r\n" );
document.write( "r = sqrt((20)^2 + (-4)^2) \r\n" );
document.write( "r = sqrt(400 + 16) \r\n" );
document.write( "r = sqrt(416) \r\n" );
document.write( "r = 2*sqrt(104) ≈ 20.396\r\n" );
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document.write( "θ = arctan(y/x)\r\n" );
document.write( "θ = arctan((-4)/(20))\r\n" );
document.write( "θ = arctan(-0.2)\r\n" );
document.write( "θ ≈ -0.197\r\n" );
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document.write( "The polar coordinates (in radians) are approximately (20.396, -0.197).\r\n" );
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document.write( "Try the rest on your own. \r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions or want to check your answers.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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