Polar coordinates are in the form #(r,theta)# where #r# is the distance from the origin #(0, 0)# to the point and #theta# is the angle in radians from the positive x-axis.
To find the radius, use:
#r=sqrt(6^2+(-6)^2) = sqrt(36+36) = sqrt72 = 8.5#
(some may prefer to leave it in the form #sqrt72#)
To find the value of #theta#, know that #6# is the opposite and #-6# is the adjacent side of a right-angled triangle, so:
#tan theta = 6/-6 = -1#
Therefore #theta=tan^-1(-1) = -pi/4# #rad#.
This means the polar coordinates can be expressed as #(sqrt72, -pi/4)# or #(8.5, -0.79)# or (to give a positive value to #theta#) as #(sqrt72, (7pi)/4)#.
