Nice to see more articles on the topic! Here is my own take at it: https://roman-suzi.medium.com/good-software-developer-uses-math-9954b46e50a1

For me math is more a way of creative thinking than specific areas like trigonometric functions you are using as an example.

I have a new insight after reading your article. Math is like a squared paper for programming. It helps the system programmers build to perfectly align, even when parts are on the opposite side of the "paper". It gives a grid, tidy lines to design your code.

It may be not that obvious in the simple questions like interview questions, but it is of real help in bigger projects to be able to grasp the system complexity by having in mind mathematical constructs, which are used.

For example, Haskell leverages Category theory heavily, making different parts of it align like magic.

Maybe, just maybe interview questions for programmers should somehow reveal a candidate's ability to be at home with abstractions (to see them in the requirements), move like a spider across abstraction levels, use some sort of symbolic calculus to simplify "formulae", which will be later used as a concise backbone of the system.