How do you convert #(-4,-4)# into polar form?

To convert between polar and rectangular, these formulas will help you out. (Link to the webpage I got the image from is in gray.)

So we can see that where the Cartesian/rectangular ordered pairs follow the #(x, y)# format, polar ordered pairs follow #(r, theta)#.

The steps here can vary, depending on whether you want to find #theta# or #r# first, but we'll just find #theta# first for this answer.

#tantheta = (-4)/-4 = 1#
#arctan(1) = 45°#

We should note, however, that since #x# and #y# are both negative, our point is in quadrant #III#. #45°# is just the reference angle. #theta# is actually #225°#.

We can use one of the left-hand formulas to find #r# now.

#-4 = rcos225°#

#-4 = r((-sqrt2)/2)#

#r = -4 * 2/(-sqrt2) = (-8)/(-sqrt2) = (-sqrt2^6)/(-sqrt2) = sqrt2^5 = 4sqrt2#

So we have found our answer: #(-4, -4)# in polar form is #(4sqrt2, 225°)#.

Of course, the way you write your answer is going to depend on whether they want #theta# in radians or degrees and whether they want you to be exact with #r# or round, but you get the gist, hopefully.