How do you convert x=3 to polar form?

2 Answers
Feb 11, 2016

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)

Feb 11, 2016

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