So whats the relationship between an angle and its sine? I typed out all the degrees between 0 and 89 into a spread sheet and wrote out the answer then made a graph. Using the mighty powers of excel I got equations for the graph. I had the option of choosing how many polynomials I wanted in my function. here is the one to the order of two: y = -0.0001x2 + 0.0208x - 0.0227 Here is the one to the order of six: y = 2E-13x6 - 4E-11x5 + 6E-09x4 - 1E-06x3 + 5E-06x2 + 0.0174x + 1E-05 each one of these will allow me to put in lets say 10 degrees and get an answer of 0.1753 or 0.17357 or 58 degrees and get an answer 0.88018 or 0.8473 These are approx what the sine of 10 or the sine of 58 degrees should actually be. So if my calculator was ever destroyed and my log tables burned I could use this to approximate the sine of any angle. Has anyone studied this? As sine and cos and tan are so prevalent in education systems every website I google is just covering them as buttons or commands or magic spells one presses and the calculator does the action behind the scenes. I wanted to know more about the action but am out of ideas of what to Google. sine 30 = 0.5 so i know the ratio of the opposite side to the hypotenuse is always 0.5. So any time I come across 30 degrees I can get sine 30; a magical spell that returns 0.5 so I know what to do with the the two sides if I compare them. Is there actually a function that is listed as official definition? What would one do if they had to program a calculator?