given $x,y$ and $\theta$, calculate its distance to origin $(0,0,0)$

Question

Apologies if this question sounds really dumb, but I am faced with a set of points:

$x_1,y_1,\theta_1$

$x_2,y_2,\theta_2$ ..

and I am looking to work out the distance between each row $(x_1,y_1,\theta_1)$ to the origin $(0,0,0)$. I have not encountered this before and I was wondering what the formula for compute this would be. A google search does not seem to reveal a lot :(

@Bernard thank you for this. This image shows what theta is: https://pasteboard.co/JpP7Slh.png I dont know if theta helps to find the distance (assuming some form of speherical coordinate). Hence my question! — AJW, Sep 06 '20 at 12:25
But your image is in the $(x,y)$ plane. It has nothing to do with a 3d space. — Bernard, Sep 06 '20 at 12:30
@Bernard yes you are right, this is what is confusing me :( from the image, it just looks like a 2D field :( — AJW, Sep 06 '20 at 12:32
Would per chance, in a better drawn figure, θ be the inclination angle w.r.t. the $z$-axis? — Bernard, Sep 06 '20 at 12:41

score 0 · Answer 1 · answered Sep 06 '20 at 12:24

0

Using Pythagoras' theorem I would say that for the first set it is equal to $$\sqrt{x_1^2+y_1^2}$$ if I have understood you correctly?

answered Sep 06 '20 at 12:24

A-Level Student

6,520

Hey, thanks for this, but they are speherical coordinates, not caterisian. – AJW Sep 06 '20 at 12:26
@AJW I didn't realsie, you should say so in the question probably, unless the angle specified makes it clear (I've never done spherical trig before, i don't know). – A-Level Student Sep 06 '20 at 12:28
I have updated the question, apologies for the confusion. – AJW Sep 06 '20 at 12:30

given $x,y$ and $\theta$, calculate its distance to origin $(0,0,0)$

1 Answers1