In HS trig class I asked the teacher what was the actual logic behind the tan function, and she said “well it’s just programmed into your calculator” and I said I realized that but how did it work, she told me to go ask the AP calc teacher.
A lot of malls in Asia have signs that say not to walk on the escalators. So yeah I guess if it breaks you’re SOL if the people in front of you aren’t rule breakers.