Question

How do you convert x=3 to polar form?

Answer 1

Oddly enough the point `(3,0)` in polar coordinates is still `(3,0)`!

Explanation:

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)`

Answer 2

It can be expressed:

`r cos theta = 3`

Or if you prefer:

`r = 3 sec theta`

Explanation:

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`