calculate x,y positions in circle every n degrees

Question

I am having trouble trying to work out how to calculate the $(x,y)$ point around a circle for a given distance from the circles center.

Variables I do have are:

constant distance/radius from center ($r$) the angle from $y$ origin

I basically need a point ($x$ and $y$) around a circle every $18$ degrees.

Excuse me if this is a very basic question but math is not my strong point :/

Ta John

Answer 1

x = radius *  cos(angle)
y = radius *  sin(angle)

Inverse Y-axis:

x = radius *  sin(angle)
y = radius * -cos(angle)

If radians is used then

radian = angle * 0.0174532925

and

x = radius *  cos(radian)
y = radius *  sin(radian)

Radian is the standard unit of angular measure, any time you see angles, always assume they are using radians unless told otherwise.

Answer 2

I'm assuming you have a calculator.

1. Enter 90; press the "cos" button. If you get "0", your calculator is working in degrees, and you're good to proceed with the rest of these instructions. If not, see if you can find a "D/R" or "DRG" button and press it once; then try again. (This converts the calculator from "Degrees" to "radians". Once you get it saying $\cos(90) = 0$, proceed.

2. for each number $i$ between $0$ and $19$, you're going to do the following. I'll illustrate with $i = 3$, and assuming your radius is 38.

   a. Enter i (I enter 3); write down i on a piece of paper

   b. Multiply by 18 (I get 54)

   c. Press the "cos" button (1 get .8090)

   d. multiply by the radius (in my case, 38; I get 22.33) and write down the value

   e. Enter i again

   f. multiply by 18

   g. press the "sin" button

   h. multiply by the radius; write down the value.

When you're done, you should have a table that looks like this:

i     x      y
0     38     0
1     36.14  11.74
2     30.74  22.33
...

which contains the coordinates that you need.