Solving an annoying equation

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Mark is attempting to convert pixel coordinates to geographical latitude and longitude in Microsoft's Virtual Earth but is struggling with the equation a = (1 + sinLatitude) / (1 - sinLatitude). He seeks assistance in expressing "sinLatitude" in terms of "a." A user responds with the solution, stating that sinLatitude = (a - 1) / (a + 1) appears to be correct after testing. Mark confirms that this solution works for his needs. The discussion highlights the challenge of mathematical conversions in programming.
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[SOLVED] Solving an annoying equation... please help

Hi,

I'm playing with the code used to convert between on-screen pixel co-ordinates and geographical lat-lon in Microsoft's Virtual Earth. They have a page that explains how to go one way (including example code) at http://msdn2.microsoft.com/en-us/library/bb259689.aspx" but it only explains how to get the pixel co-ordinate from a lat-lon and not the other way around.

I decided it shouldn't be too difficult to solve myself so I started on it. I'm now stuck at the following point:

a = (1 + sinLatitude) / (1 - sinLatitude)

I need to calculate "sinLatitude" in terms of "a" but I don't seem to be able to do it. Can anyone please give me some pointers, or do I need to approach the whole thing another way?

Many thanks,

Mark
 
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Is sinLatitude = (a-1)/(a+1) the answer you are looking for?
 
After running a few tests, it certainly seems to be!

Many thanks for your help!

Mark
 
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