Why do we still teach a semester of trigonometry? How about engineering instead?

Arthur Benjamini says we should teach statistics before calculus.  He points out that most of what we do in high school math is preparing us for calculus. He makes the point that while physicists, engineers and economists need calculus, in the digital age, discrete math, probability and statistics are much more relevant to everyone else. I agree with him and was happy to see Statistics as part of the common core. However, other topics I wish were there, such as engineering, programming, and finance, are missing.

This saturday I took my 5th grader to a 3 hour robotics workshop. We both enjoyed it thoroughly. We built and programmed two-wheeled robots to, among other things, go around a table. To make this happen we learned about measurement error,  how to use a protractor, that C =   ∏ d, a bit of algebra, how to use grid searches, if-else conditionals, and for-loops. Meanwhile during a semester of high school trigonometry we learn this (do you remember that 2 sin^2 x = 1-cos 2x  ? ). Of course it is important to know trigonometry, but do we really need to learn to derive and memorize these identities that are rarely use and are readily available from a smartphone? One could easily teach the fundamentals as part of an applied class such as robotics. We can ask questions like: if while turning you make a mistake of 0.5 degrees, by how much will your robot miss its mark after traveling one meter? We can probably teach the fundamentals of trigonometry in about 2 weeks, later using these concepts in applied problems.