That's not even simplifying it, it's just changing it into a rarer trigonometric function and making it less readable
And who uses "o" as a variable? Basically guaranteed unreadability.
Whatever math detector they're using is hair-trigger and wrong.
And who uses "o" as a variable
Scientists who aren't mathematicians, usually.
It's fine if you're working with things more abstract than numbers. You see O used in computational complexity notation all the time, and O is often used for a structure sheaf which will vary based on context, like in algebraic geometry. I think in general really it's not an issue as long as you're not discussing functions where the reader might consider that zero could be a possible input, like trigonometric functions for example.
Never understood why we're taught specific names for these trig functions rather than just expressing them all in terms of sine and cosine
Alternatively, one could just use cos(x-90) in place of sine. Since it's arbitrary which we throw out, I say keep them both (also it allows you to intuitively associate sine and cosine with the legs of a right triangle in the unit circle)
I'm not sure why cos gets a pass but 'csc' doesn't. I'd absolutely argue the opposite in terms of intuitive associations.
I'd say sine and cosine get priority because they are much more well behaved and easier to work with than their reciprocals full of asymptotes and discontinuities
What's wrong with degrees? Everybody understands them and they're whole numbers that are easy to work with.
Nothing wrong with degrees, they are definitely more useful for engineering and practical applications in many cases. But while doing math for math's sake, radians feel much more elegant because pi is a fundamental result of our axiomatic system whereas degrees are totally arbitrary numbers picked for convenience.
Maybe it was back in the day people would rather remember shorthands for csc and such rather than having to write it out long form each time. (I agree with your point tho I'd rather not have to memorize those)
Because before calculators, people used to had books with a buch of tables with the values of each function and their solution. So, having sen and csc given is easier than having to solve 1/sin
Edit: here's an excellent video about one of these books: https://youtube.com/watch?v=OjIwCOevUew
Arsenio Hall is an American comedian, actor and talk show host. He hosted the late-night talk show, The Arsenio Hall Show, from 1989 until 1994, and again from 2013 to 2014. He has appeared in Martial Law, Coming to America, Coming 2 America, and Harlem Nights.
