How do you calculate a sine? (Historical question)

I have a Minitran card, depicted below. It was in use around 1969 for teaching Fortran to school students.

You used it by using a bent paper-clip to punch out chads corresponding to what you wanted. For example, the "IF(" chad for an IF statement.

As I recall, there were only variables starting with A, B, I, J (probably followed by one or more numbers). As you can see, the other letters of the alphabet, except F, are not present.

I seem to remember you could calculate trigonometric functions like Sin, Tan, Cos, etc. But how? Does anyone remember these, and how you would do it? A possible way would be to use the F chad, eg. F1 = Sin, F2 = Cos, F3 = Log, etc.

If anyone knows how this was done, I'd appreciate hearing. Googling for answers hasn't been very helpful.

things like these make me to think about Mr. Babbage
and his "new reality engine" for calculating and printing
mathematical and astronomical tables

sorry, I don't have an answer to your question,
here I use Taylon, when applicable

at the end of one of my math book I have a long printed table
where the sine is pre calculated, by a Taylor series,
with a predefined step

Nightmares!
I was fixing card punches/readers then.
Hands bled regularly.

Mask that image now!

Hi,
Taylor Series Approximation.

Tan = Sin / Cos

Tom... :slight_smile:
PS. I had some very good mathematics teachers during HSC.

10sTaylorPolySeries.pdf (132 KB)