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When I was looking for info on converting latitude/longitude to $(x,y)$ Cartesian coordinates, I found this link on Doctor Math.

I found this following formula:

In Radians: $$x = (\text{lon}_2 - \text{lon}_1)\times \cos(\text{lat}_1)\times \frac{\pi}{180}$$ $$y = (\text{lat}_2-\text{lat}_1)\times \frac{\pi}{180}$$

In miles: $$x = (\text{lon}_2-\text{lon}_1)\times \cos(\text{lat}_1)\times \frac{\pi \times R}{180}$$ $$y = (\text{lat}_2-\text{lat}_1)\times \frac{\pi\times R}{180}$$

And :

$$\text{lat}_2 = \text{lat}_1 + y\times \frac{180}{\pi\times R}$$ $$\text{lon}_2 = \text{lon}_1 + x\times \frac{180}{\pi\times R\times \cos(\text{lat}_1)}$$

The Question:

Why converting to radian or degree for finding x,y?
Are there any references that explain the previous conversion formula?

Thank you :)

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    Without actually looking carefully at the formulas, my first guess is that they assume that latitude and longitude are in degrees and the $\pi$ and 180 factors are there because there's some kind of arclength computation going on.2011-06-26

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