I added these two problems to the Precalculus homework list as part of my effort to incorporate science examples in my classes.
They were taken from solutions to some physics exercises and intended to give more practice on multi-variable systems. Afterwards I shared a copy with our science people accompanied by an apology. I had stripped the problems of meaning. They just sit there lifeless, without any scientific justification or reasoning. Our students will still benefit from seeing problems that are closer, if only in notation, to the ones they will see in their science courses. Anyway, if you think about it, the problems are least one level above the algebra abstraction where all variables are x and y.
I just got an email from our physics professor. He asked me to reword the first problem to emphasize that the tangent of theta is a function of several variables. What a good idea. This is a point of view that we introduce too late in mathematical curricula. I can’t wait to discuss this stuff with my students tomorrow.