It's reflected through the line y=x to make the Cartesian coordinates match up with the polar coordinates. In Cartesian coordinates, x=0 in the middle of the graph and gets larger to the right. In polar coordinates, the angle (theta) starts at 0 on the right and gets larger as it rotates counter-clockwise.
The reflection doesn't make too much of a difference to the shape of this particular graph because the function has odd symmetry (that is, f(-x) = -f(x)), but it would look "backwards" for more complicated functions.
You can do this with any graph by replacing x with theta and y with r, but it's usually done only with trigonometric functions because they're cyclical. For example, if you converted the line y=x to r=theta, you'd get a spiral.
can you do that for any graph on the cartesian system?
ReplyDeleteWhy is it mirrored first? One could just fold the x- instead of the y-axis.
ReplyDeleteAlexander N. Benner yes...same question in my mind too, as soon as I saw the complete sequence...
ReplyDeletenevertheless, it is superb animation...thanks for sharing :)
ReplyDeleteIt's reflected through the line y=x to make the Cartesian coordinates match up with the polar coordinates. In Cartesian coordinates, x=0 in the middle of the graph and gets larger to the right. In polar coordinates, the angle (theta) starts at 0 on the right and gets larger as it rotates counter-clockwise.
ReplyDeleteThe reflection doesn't make too much of a difference to the shape of this particular graph because the function has odd symmetry (that is, f(-x) = -f(x)), but it would look "backwards" for more complicated functions.
You can do this with any graph by replacing x with theta and y with r, but it's usually done only with trigonometric functions because they're cyclical. For example, if you converted the line y=x to r=theta, you'd get a spiral.
I like to watch the animation, thank you. What is it good for?
ReplyDeleteUh oh, here we go again. Good one! :-)
ReplyDeleteA bunch of good ones on this page....
ReplyDeletehttp://en.wikiversity.org/wiki/Polar_Coordinates