126
The US is COOKED
(hexbear.net)
https://www.nationsreportcard.gov/highlights/ltt/2023/
The confluence of societal and governmental factors leading to these outcomes is an irredeemable tragedy. Nobody gives a fuck about education and the consequences are accelerating
I don't think there is a reasonable way to calculate trigonometric functions by hand. The computer solves a number of terms in an infinite series to approximate it. Back in the day there used to be books of tables, that had a lits of trigonometric functions logarithms, and so on for different numbers. I guess you could also use a slide rule. As a side note, there is an old timey isekai by an American author, I forget the name, were the magician has to give up his magic to get a book of tables and it's considered a good deal.
The closer thing to solving trigonometric functions by hand that can be taught in grade school is the unit circle. Incidentally when you buy a ruler set, it comes with 2 triangles and a compass, the 2 triangles have 30 and 45 degree angles Wich are the ones used for the unit circle.
all correct, there is not a nice work around for general computation of trigonometric functions. this is partly why the algebra of trigonometry is emphasized. the closest one might find to simple reasonable approximations of trig functions are the approximations one uses in physics for "small angles" which is a trick employed to get a model out of a differential equation without a solution in terms of elementary functions. so for "small angles" one can substitute
xforsin xand1forcos x.