Polar Coordinates

Those of you who have been studying the Cartesian Coordinate system for years might feel a bit uncomfortable leaving the realm of (x,y) and entering the space of (r, theta). I have found some things that might make you feel more comfortable, or at least a little less wary.




Remember those childhood days you spent at the playground, swinging, sliding and climbing on those rope ladders?  You may have thought those ropes were supposed to look like spider web, but in fact they were simply preparing you for your high school math class, when you entered the polar coordinate system.  Just look at all those radii and angles.  Now do you feel better?

 








 

Alternatively, you can imagine a red face plastered behind the circles and spokes.  If Spidey has embraced it, so can you!!!



   













Use this link to play around with functions in polar coordinates.  www.shodor.org/interactivate/activities/PolarCoordinates/ 

Input a function and then click on the plot/update button to see what the graph looks like or create a table of coordinate points.  Try a variety of sine, cosine and tangent functions, such as sin(2*t), tan(4*t), cos(0.3*t).    Try inputting large values (>100) for theta maximum and see what happens to your graphs.  What do you notice?  Why do you think this happens?