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This is not the problem in itself but it is related to something I'm doing.

I need to find a formula for the average angle of a latitude on earth w.r.t. the sun. e.g. if the earth was not inclined by 23.5 degrees, the average angle would just be the lattitude. Instead, 30 degrees north is effectively between 30+23.5 degrees and 30-23.5 degrees. In this case, the average angle is simply 30 degrees but this changes if the lattitude is less than the rotational inclination.

e.g. at the equator (0 degrees), is between 23.5 degrees and -23.5 degrees. Just taking the average you get 0 degrees, where the average is half 23.5 (as going down to -23.5 is the same as going down to 0 and then back up to 23.5). Am I missing something simple?

To sum up I'm looking for a function where I can input a lattitude and get back an average effective angle (which should equal the lattide for lattitudes larger than the rotational inclination (23.5), half 23.5 for the equator, something in between for stuff in between. Can I do this logically or do I have to be more clever? (integral etc.)

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# Average annual angle (Earth lattitude)

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