# How do I reliably find this point of a sector, regardless of the arc angle?

I'm doing some programming and when I was working angles of rotation, I have found that I need to be able to find a certain point of a sector regardless of the arc angle. It is something that I've found to have difficulty with. Finding the sector length doesn't tell us anything that leads to finding out this.

I need a solution that is able to stand up to all various different scenarios, such as different angles and positions on the circle.

The values in the example picture below, are just for explanatory purposes.

Circle example: http://i.imgur.com/Nf638.png

Thank you.

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What does the "$\Delta,0$" mean in your diagram? What does the "$0.50$" mean in your diagram? – Gerry Myerson Feb 25 '12 at 4:27

## 1 Answer

I'm going to guess that what you really want is something like this. (If this isn't what you really wanted, please edit your question to clarify).

• I have a circle centered at 0,0
• The radius of the circle is R (in this example, R=50 meters).
• I'm at the center of the circle facing due North. Then I turn clockwise to a bearing A degrees from true north.
• What point X, Y on the circle am I looking at? (Where positive X is East of center, and positive Y is North of center, as normal).

Then

• X = R*sin(A)
• Y = R*cos(A)
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