How does the location of sunrise and sunset change throughout the year? (Advanced)

The sun appears to rise on the eastern horizon and sets on the western horizon. How much does the location of the sun rising and setting change throughout the year and depending upon where your viewpoint is, i.e., true East, true West, etc.

Irrespective of where you are on the globe, the Sun will always rise exactly East and set exactly West on two days: March 21 and September 21 which are the two equinoxes. As to the second part, it is a little complicated:

Consider an arbitrary location on Earth (to make matters simple, consider a place in the northern hemisphere). Now, the celestial north pole (where the star Polaris resides) will be at an angle above the horizon and the angle is exactly equal to the latitude of the place. Imagine yourself facing Polaris (so that you are facing north exactly). Then East will be to your right and West will be to your left. Now, draw a circle which passes through East and West and whose plane is exactly perpendicular to the line joining you and Polaris. This circle marks the path of the Sun from dawn to dusk on the two equinoxes.

Now, draw a circle which is exactly parallel to the first circle, but which are separated from the first circle by 23.5 degrees at the zenith towards Polaris. This marks the path of the Sun during summer solstice and the place where this circle cuts the horizons will mark the place where the Sun will rise and set on the day of summer solstice. A similar circle which is separated from the first circle by 23.5 degrees at zenith towards south will mark the path of the Sun on winter solstice.

Thus, the Sun will rise north of true East and set north of true West during summer whereas during winter, the Sun will rise south of true East and set south of true West.

The exact location where the Sun will rise and set will vary widely depending on the place. Beyond the Arctic circle, there will be some times of the year where the Sun stays in the horizon for all 24 hours.