First question, here goes!
In respect to, How to calculate opposite direction angle
I am currently trying to find a non Taylor-series/non calculator method to calculate (in degrees) sine, cosine and tangent-- quickly and efficiently by hand.
So far, I have only tried experimenting with an algebraic formula I happened to make, that attempts at finding the sine of a degree angle to the ten-thousandths place.
For example, "Find the Sine of 60 degrees"
I tried conjuring up a draft of a formula, but I have the slightest clue on how to find the adjacent angle algebraically;
deg. = degrees
n = math.sign of 180;
meaning, if "n" is greater than or equal to a 180th degree, then "n" = -1. else if "n" is less than or equal to a 180th degree, then`"n" = 1.
(I say "180th degree" instead of "180 degrees" in case the angle plugged into the formula below is equal or greater than 360 degrees or below zero degrees)* , then n = -1.***
If sine = opposite/adjacent and opposite =(deg. + (180 * n)) then
sine = (deg. + (180 * n))/adjacent
Any help would be greatly appreciated!
Some other postulates
Hypotenuse = adjacent/cosine
Adjacent = opposite/tangent