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$$ x = \cos(lat_1) * \sin(lat_2) - \sin(lat_1)*\cos(lat_2)*\cos(long_2-long_1) $$

$$ y = \sin(long_2-long_1)*\cos(lat_2) $$

The angle is calculated by taking as base the north geographic pole.

How to know the time with a compass and azimuth of the sun?

Every hour, the Earth rotates on itself about 15 degrees, so every hour on Earth, we see the sun 15 degrees further west.

By knowing the azimuth of the sun, we can deduce the time. At noon, the sun is 180 degrees. Each difference of 15 degrees is 1 hour.

Consider the azimuth of the sun at 165 degrees. It is therefore around 11 am.

Consider the azimuth of the sun at 210 degrees. It is thus about 2 pm.

The given time is Solar Time.

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