Converting polar coordinates to rectangular coordinates

Question

Convert angle in degrees to a point

How could I convert an angle (in degrees/radians) to a point (X,Y) a fixed distance away from a center-point.

Like a point rotating around a center-point.

Exactly the opposite of atan2 which computes the angle of the point y/x (in radians).

Note: I kept the original title because that's what people who do not understand will be searching by!

hi, i have polar cordinates for north pole. how to convert it to Lat-long? — Pragnesh Patel, Jan 04 '10 at 09:11
@PragneshPatel [Altitude = `r`, Latitude = `180°-θ`, Longitude = `φ`](https://en.wikipedia.org/wiki/Spherical_coordinate_system). You may want to multiply the lat and long by `180/π` to convert them to degrees. — JamesTheAwesomeDude, May 03 '21 at 08:36

score 22 · Accepted Answer · answered Jan 29 '09 at 05:19

22

Let the fixed distance be D, then X = D * cos(A) and Y = D * sin(A), where A is the angle.

answered Jan 29 '09 at 05:19

PolyThinker

`function pol2rect(r, θ) { return [r * Math.cos(θ), r * Math.sin(θ)]; }` – JamesTheAwesomeDude May 03 '21 at 08:41

score 4 · Answer 2 · answered Jan 29 '09 at 05:55

4

If center-point (Xcp, Ycp) isn't the origin you also need to add it's coordinates to (X,Y) i.e. X = Xcp + D * cos(A) and Y = Ycp + D * sin(A)

answered Jan 29 '09 at 05:55

jeffD

score 2 · Answer 3 · answered Jan 29 '09 at 05:20

2

What PolyThinker said.

Also, if you need the distance from the origin, it's sqrt(x^2 + y^2).

answered Jan 29 '09 at 05:20

Sophie Alpert

score 1 · Answer 4 · answered Jan 29 '09 at 05:19

1

t = angle
r = radius (fixed distance)

x = rcost
y = rsint

answered Jan 29 '09 at 05:19