You might get that through other methods besides trig, meaning trig isn't strictly necessary -- it's just one option among potentially many. The hard part is proving efficacy and efficiency of each option.
CompSci interview questions go way beyond loops, conditionals and recursion though, such that if you don't already know some secret sauces, it's unlikely to get the best case solution that the interviewer wants.
The other thing throwing this off is interviews are looking for different grades of solutions or maybe just looking at your problem solving/communication skills, e.g. you can fail to find the best known solution but still get a job because of your reasoning.
So in this way, the algorithms & data structures interviews can sometimes be used to test knowledge, or test problem solving ability, or both.
The interview stopped being a test of "if you can do this job" and instead seeks to find a correlation backed up by some research that says "people that prepare, study, and do well at this interview also do well at this company". Similar research meant that they needed to stop asking brain teaser questions because it wasn't a good indicator of success.
Perhaps the knowledge of data structures and algorithms can be useful for people who need to design whole architectures and systems, but I think the folks who are fixing bugs, tweaking the UI, or adding small features would benefit more from Code Complete than an Algorithms book.
Sometimes its good to accept that the uncertain things are uncertain.
If i were them, i would find and train good "screeners", people with talent to spot talent and just let them do the job. Sometimes they will only have a hunch, giving their observations of things that escape most people of a particular candidate, and even without much to show of, they might be right.
Later the top screener's would help the new ones to be better at their job, teaching their tricks.
This is very subjective and personalized, and even if there might be some objective ways to train the screener's better, i think its just nuts trying to use objective tests to define a good hire.
I bet with you that there are a lot of "human gold" out there that would only be detectable only when its too late for the company.
There seems to be more emphasis on "the candidate knew to use bubble sort" or something stupid like that instead of "I observed this candidate reason through the problem and I don't really care that they didn't know a canned algorithm".
It's a bad proxy, but better than no proxy in my opinion.
You often need strange problems to really get to see people's problem solving, which is why they're often not things you see in real life, but again, the goal isn't to see if people know how to do the strange thing, it's to see how they approach a novel problem from scratch. Aka problem solving skills.
Explaining your abstract, critical thinking process seems much more valuable. HR screens someone for having the degree, assume they are familiar with all the facts (they can use Stack Overflow when they get in). Just learn how they think and how they communicate.
(In past tense because this "Microsoft interview" style quiz was dropped by Microsoft themselves long ago)
Isn't that similar to people saying "I've never used trig in 30 years"? Isn't the point to train your brain to think in a certain way, more so than actually needing sines and cosines?
For computer science specifically, the goal is to teach you to think in terms of loops, conditionals, recursion and so on. It's to train the muscle more so than memorize specific algorithms or data structures.