Azimuth

 The role of the arccos function is to capture how long the sun is at

work on a particular day. One needs to appreciate the notion of azimuth

on the plane on which the observer stands.

                                                                    

source: Math is Fun

Gemini: 

The arccos term measures the solar hour angle at the exact  moment of

sunrise or sunset.

                                                                     

For Paris on the summer solstice, the sun travels some 120 degrees.

from the moment the Sun is highest until it dips below the horizon.

Meta ai:

It's half the daylength in angular units. You multiply it by 2 and convert angle to time to get total daylight.

                                         *     *     *

624 - 546 BC

*     *     *

570 - 495 BC

*     *     *

190 - 120 BC

                                                            

*     *     *

https://youtu.be/G1IKTyNXPUA?si=kV4ful3fqqYw7Ln7

Doing the math on 25 degrees...

tan(25 degrees) = .4663

tan(23.5 degrees) = .4348

Multiply: 

.4663 x .4348 = .2028

Find the angle:

arccos(.2028) = 1.775 rad

                       = 101.7 degrees

Convert to hours:

2/15 x 101.7 = 13.56 hours

We are in winter:

24 - 14 = 10 hours