Calculating Sines without Calculus

Sunday, June 3rd, 2012

One of my better math teachers in high school was John Brumfield. He taught me Algebra I and Precalculus. He was also exceptional at calculation, a skill that got him into in the artillery core in World War II, where he had to calculate gunnery firings in real time. And he had a great sense of humor. But one of the things that stands out most clearly in my memory from one of his classes is something he may have gotten wrong (perhaps deliberately). At that point in the early 1980s scientific calculators existed, but were quite expensive and not yet integrated into the high school mathematics curriculum. We were probably one of the last classes to spend significant time learning about trig tables, and how to interpolate between values. (A surprisingly useful skill, by the way, even if the reason we learned it no longer applies.) I recall that someone in the class asked him how the numbers in the tables were calculated. E.g. how did the author know that the sine of 47.1 degrees was 0.0238875315 and not 0.0238875326 or some other value? And his answer still sticks with me to this day, and I quote it word for word: “Very accurate graphs”.