document.write( "Question 1043084: Sketch a graph of the polar equation, and express the equation in rectangular coordinates.\r
\n" ); document.write( "\n" ); document.write( "θ=-pi/2 \n" ); document.write( "
Algebra.Com's Answer #658181 by Edwin McCravy(20064) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This is one that you can't use the usual formulas \r\n" );
document.write( "to convert with.  You must understand how \r\n" );
document.write( "polar graphs work.  I'll show you what you must\r\n" );
document.write( "do when the formulas won't work:\r\n" );
document.write( "\r\n" );
document.write( "There is no \"r\" in this equation, however\r\n" );
document.write( "you could think of it as having the term 0r,\r\n" );
document.write( "like this\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then you can get a few polar points\r\n" );
document.write( "\r\n" );
document.write( " r | θ\r\n" );
document.write( "---------\r\n" );
document.write( " 1 | -π/2    (r,θ) = (1,-π/2)  \r\n" );
document.write( " 2 | -π/2    (r,θ) = (2,-π/2) \r\n" );
document.write( " 3 | -π/2    (r,θ) = (3,-π/2) \r\n" );
document.write( "-1 | -π/2    (r,θ) = (-1,-π/2) \r\n" );
document.write( "-2 | -π/2    (r,θ) = (-2,-π/2) \r\n" );
document.write( "-3 | -π/2    (r,θ) = (-3,-π/2) \r\n" );
document.write( "\r\n" );
document.write( "The polar point (r,θ) means to swing a radius line around through the\r\n" );
document.write( "angle θ, counter-clockwise if θ is positive and clockwise if\r\n" );
document.write( "θ is negative.  Then go out on that radius line as many units as \r\n" );
document.write( "the value of r in that direction.  If the value of r is \r\n" );
document.write( "positive, you go out away from the origin (or pole).  If the\r\n" );
document.write( "value of r is negative you go backward through the origin\r\n" );
document.write( "or pole.\r\n" );
document.write( "\r\n" );
document.write( "Using polar graph \"spider-web\" paper, this is how you plot the \r\n" );
document.write( "polar point (r,θ) = (2,-π/2).\r\n" );
document.write( "\r\n" );
document.write( "Starting for the \"east\" (right side of the horizontal, \r\n" );
document.write( "swing around through π/2 radians or 90° CLOCKWISE \r\n" );
document.write( "since θ is NEGATIVE, indicated by the red arc,\r\n" );
document.write( "then go out 2 units, along the red line, and plot a point.\r\n" );
document.write( "Normally we don't show the red arc or the red line to keep\r\n" );
document.write( "from cluttering up the graph, but I'll do it for this \r\n" );
document.write( "illustration:\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "----\r\n" );
document.write( "Using polar graph paper, this is how you plot the polar point\r\n" );
document.write( "(r,θ) = (-3,-π/2).\r\n" );
document.write( "\r\n" );
document.write( "Starting again for the \"east\" (right side of the horizontal, \r\n" );
document.write( "swing around as before through π/2 radians or 90° CLOCKWISE \r\n" );
document.write( "since θ is NEGATIVE, indicated by the red arc,\r\n" );
document.write( "but this time how you go out is different.  You go out 3 units, \r\n" );
document.write( "but this time BACKWARDS through the origin along the red line, \r\n" );
document.write( "which goes BACKWARDS through the origin and plot a point.  That's\r\n" );
document.write( "because the value of r is NEGATIVE.  Like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "When all the points are plotted we have this:\r\n" );
document.write( "and when we connect all those points we have this vertical \r\n" );
document.write( "line:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now if we superimpose rectangular graph paper\r\n" );
document.write( "on the \"spider-web\" graph paper, we get this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As you see, the graph is the line which is the y-axis.\r\n" );
document.write( "And the rectangular equation of the y-axis is \r\n" );
document.write( "\r\n" );
document.write( "x = 0      <-- that's the rectangular equation for \r\n" );
document.write( "\r\n" );
document.write( "If you need to ask me any questions about this, feel free \r\n" );
document.write( "to ask them in the thank-you note form below.  I'll get back\r\n" );
document.write( "to you by email.  (no charge ever. I do this as a hobby).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );