How do you convert x=3 to polar form?

Question

How do you convert x=3 to polar form?

2 Answers

Impact of this question

44949 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-11T19:51:18

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

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 $(r, θ)$ $(r, \theta)$ were $r$ $r$ is the straight line distance back to the origin and $θ$ $\theta$ 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 $0^{o}$ $0^o$ / $0$ $0$ radians ( or $360^{o}$ $360^o$ / $2 π$ $2 \pi$ radians).
Formally this is because the $arctan (\frac{0}{3}) = 0$ $arctan (0/3)=0$ radians or $0^{o}$ $0^o$ (depending on what mode your calculator is in).
Recall, $arctan$ $arctan$ is just $tan$ $tan$ backwards.
Thus $(3, 0)$ $(3,0)$ in polar coordinates is also $(3, 0)$ $(3,0)$ or $(3, 0^{o})$ $(3,0^o)$

Answer 2 · 2016-02-11T19:59:47

It can be expressed:

$r cos θ = 3$ $r cos theta = 3$

Or if you prefer:

$r = 3 sec θ$ $r = 3 sec theta$

Explanation:

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

$x = r cos θ$ $x = r cos theta$

$y = r sin θ$ $y = r sin theta$

In our example $x = 3$ $x = 3$ becomes $r cos θ = 3$ $r cos theta = 3$

If you divide both sides by $cos θ$ $cos theta$ then you get:

$r = \frac{3}{cos θ} = 3 sec θ$ $r = 3/cos theta = 3 sec theta$

Science

Math

Humanities

... and beyond

How do you convert x=3 to polar form?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question