You can even convert between the two if you want to.Īlternatively, you could convert polar coordinates to rectangular coordinates #(x,y)# to graph the same point. #theta# is typically measured in radians, so you have to be familiar with radian angles to graph polar coordinates. The convention is that a positive #r# will take you r units to the right of the origin (just like finding a positive #x# value), and that #theta# is measured counterclockwise from the polar axis. To graph them, you have to find your #r# on your polar axis and then rotate that point in a circular path by #theta#. Polar coordinates are in the form #(r,theta)#. This graph has equation: #r(theta)=e^sqrt(theta)#Īs you can imagine this would be considerably difficult to work with in Cartesian.īut anyway, that is general idea of a polar plot. Polar plots can also be used to produce some interesting spirals as well, So a line drawn from the origin at 60 degrees from the #x#-axis will meet the ellipse when the length of that line is 1. If the graph has some form of circular symmetry then perhaps polar may be advantageous over Cartesian.Īt an angle of #60^o# from the x-axis this would have a value: Whether or not you wish to use polar coordinates really depends on the situation.
a function that links #r# to #theta# as appose to a function that links #y# to #x#). So a polar plot is quite simply plot where the function has been written in polar form, (i.e.
The diagram below provides a simple illustration of how a point can be expressed in either Cartesian or polar coordinates.įrom this we can also see how to convert between polar and Cartesian coordinates using simple trigonometry: In polar coordinates we write the coordinates of a point in the form #(r,theta)# where #r# is the distance directly between the point and the origin and #theta# is the angle made between the positive #x#-axis and that line. When we write coordinates in the form #(x,y)# we call them Cartesian coordinates. In this plot, every value along the #x# axis is linked to a point on the #y# axis. Consider a typical plot that you will have came across before: