How do you convert x=3 to polar form?

This is a somewhat incomplete question.
Do you mean express the point written in Cartesian coordinates as x=3 y=0 or (3,0) in polar coordinates or the vertical line x=3 as a polar function?

I'm going to assume the simpler case.
Expressing (3,0) in polar coordinates.
polar coordinates are written in the form #(r, \theta) # were #r# is the straight line distance back to the origin and #\theta# is the angle of the point, in either degrees or radians.

The distance from (3,0) to the origin at ( 0,0) is 3.
The positive x-axis is normally treated as being #0^o# /#0# radians ( or #360^o#/ #2 \pi# radians).
Formally this is because the #arctan (0/3)=0# radians or #0^o# (depending on what mode your calculator is in).
Recall, #arctan# is just #tan# backwards.
Thus #(3,0)# in polar coordinates is also #(3,0)# or #(3,0^o)#

To convert an equation in rectangular form to polar form you can substitute:

#x = r cos theta#

#y = r sin theta#

In our example #x = 3# becomes #r cos theta = 3#

If you divide both sides by #cos theta# then you get:

#r = 3/cos theta = 3 sec theta#