# Finding coordinates of a point in a circle with angle

#### AlicanC

I have a point (x,y), a distance (d) and an angle (a). I need a method to find a point using x,y,d and a. For example:
http://c.imagehost.org/0836/03082008299.png [Broken]
I will apply this on a 3D environment, but I am not going to use the 3rd dimension so it's safe.
This is also about programming, but I am capable of applying methods in the programming language so I asked it here.

Last edited by a moderator:

#### ZharAngel

$$(x_?,y_?) = (x+d\cos\alpha,y+d\sin\alpha)$$

#### AlicanC

Thanks for the answer, but I have a problem. I wrote some code to put this in action. The code starts from "0" and adds "20" to the angle until the vaule is greater than to "360". I don't know why but the code produced this:
http://c.imagehost.org/0346/2008-08-03_092702.png [Broken]
As you can see there are some mistakes. All are getting repeated but the ones I marked. Here is the debug output I get:
(1) Center of the circle located at (-49.013168, -1082.446166)
(1) Drawing at (50.986831, -1082.446166) Angle is 0.000000
(1) Drawing at (-8.204959, -991.151611) Angle is 20.000000
(1) Drawing at (-115.706977, -1007.934875) Angle is 40.000000
(1) Drawing at (-144.254455, -1112.927246) Angle is 60.000000
(1) Drawing at (-60.051891, -1181.835083) Angle is 80.000000
(1) Drawing at (37.218719, -1133.082763) Angle is 100.000000
(1) Drawing at (32.404930, -1024.385009) Angle is 120.000000
(1) Drawing at (-68.794525, -984.422180) Angle is 140.000000
(1) Drawing at (-146.576110, -1060.503662) Angle is 160.000000
(1) Drawing at (-108.859176, -1162.561401) Angle is 180.000000
(1) Drawing at (-0.294399, -1169.775878) Angle is 200.000000
(1) Drawing at (50.595352, -1073.606323) Angle is 220.000000
(1) Drawing at (-16.435035, -987.901672) Angle is 240.000000
(1) Drawing at (-122.032585, -1014.122192) Angle is 260.000000
(1) Drawing at (-141.187133, -1121.227050) Angle is 280.000000
(1) Drawing at (-51.222831, -1182.421752) Angle is 300.000000
(1) Drawing at (41.357345, -1125.261718) Angle is 320.000000
(1) Drawing at (26.953659, -1017.415100) Angle is 340.000000
(1) Drawing at (-77.382278, -986.554565) Angle is 360.000000
As you can see some values are too close. I am really bad at trigonometry, so I can't find the problem.

Last edited by a moderator:

#### futurebird

The center is at (-49, -1082) and your first point, with the angle, 0 is at
(51, -1082) then radius, d, is 100.

So, when the angle is 20 the point should be
$$100(\cos(20)) + -49 \approx 45$$
$$100(\sin(20))+ -1082 \approx -1048$$

But you have:

Drawing at (-8.204959, -991.151611) Angle is 20.000000

#### AlicanC

Ah, you are right! I was making calculations with radians.

Thank you both so much! I was trying to figure this out for two days! Normally I post my questions to forums related to coding or just ask my friends, but can't get an answer :D

#### ZharAngel

Always a problem if you forget. When I get errors like that, the first thing I do is to check the mode on my calculator. Lol.

"Finding coordinates of a point in a circle with angle"

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