Trigonometry

Hob's original post tells us nothing useful which is why I asked a so simple question: "So are you agreeing with what Don Kelly wrote, or saying something different?" If you don't completely agree with what Don Kelly wrote, then where is the difference. Again it is not difficult if your original post was based in basic technical knowledge.

For lurkers - I believe I have caught hob in a post he fears to justify. So instead he refers back to an original post that tells us nothing; except that hob can post like a politician. Hob can demonstrate where he disagrees with Don Kelly, or admit he had no idea - was posting about things he did not know.

Hob - I have guessed noth> Are you just guessing - that all calculators work exactly alike? >

This describes a lookup table approach that only the most naïve designer would take. Only 45° worth needs to be calculated. Do the calculations for

22.5°, 11.25° and so on in a binary way for your table. Then use sum and difference formulas to get precise values. Alternatively, your table could include interpolation formulas or Taylor expansion coefficients. The guys who hand calculated for the tables were not stupid.

---------- I have a set of log tables which gives the log(10) of sin, cos, tan,cot to 6 figures for each degree and minute, with an interpolation number per second of arc. This latter changes as the base angle changes. e.g: log(sin(5 degrees 30 minutes 20 seconds is given as

8.981573 (old notation corresponding to 10-8.98... or -1.018427 by calculator) +20*21.83*10^-6 (linear interpolation) For an angle of 35 degrees, 0 minutes the interpolation factor is 3.02x10^-6 so it appears that the table was calculated, likely by series expansion, to the nearest minute and linerar interpolation in between. The table of natural sines is carried out to only 5 places and no interpolation values are given at the "second" level (so linear interpolation is assumed if one wants it) Note these tables were originally published in 1903 and were particularly applied to railroad surveying. If you are building a spiral tunnel that is a mile long, starting at both ends, accuracy is important! I doubt whether any binary division scheme was used. Not too popular back then. The question is whether the "minute" changes were calculated by a Taylor's series or not. In any case, a lot of hand work was done and I am sure that all reasonable effort was made to minimise this.

First, you are not the original poster and it was not your question that was to be answered. Why would you think I should guide you through an answer where you cannot discern two simple differences- do you really think the NG revolves around you?

Here's a clue - Just read what Don said and read what I said and ignore what you want to see - and see what words are different. The differences are obvious.

Again it is

If you can't read simple english and see what was said, why should anyone hold your hand to guide you through it?

Ok, I'll be kind this one time, even though you take snide shots whenever asking questions -

1) The original question was where the poster could find a book on the mathematical source of the trig functions, rather than just the relationships of sides and angles.

I said there will be no in-depth material because the functions are definitions. (In math, definitions are not derived and thus have no proofs - they just are.)

What did Don kelly say about a source book? ______________

Did Don Kelly and I agree, not agree, or disagree?

2) The original poster asked how calculators find the trig functions.

I said HP calculators use series to calculate each time a function is requested

What did Don Kelly say as to HP calculators? ________________

Did we agree, not agree, or disagree?

Not bloody likely.

I did not say I disagreed with Don Kelly - I said my post did not agree with his. That does NOT mean I disagree with his post in the slightest.

or admit he had no idea - was posting about things he

Reread the original post and mine and Don Kelly's and then state your question. If your question makes any sense and seems sincere, I will answer it.

They were explained several times - the problem is that you do not read what is written and then you assume your questions were not answered.

Hell, every first quarter freshman engineering student at the U for the past

25 years has had to calculate the trig functions in class and in lab using series. It isn't some mysterious new thing most engineers haven't done in school. It's as basic as calculus. I have programmed in five languages, and I have had to do those series at least once in each language course. And program most of the calculator functions in lab. And the CRC tables used to have the equations used to get the trig tables in the header. They didn;t measure with a ruler to get the values.

And my HP handbook says how the values are derived - but since I don't have a TI. etc., source book, I can't tell you what TI or Casio or whoever uses.

Or

Right on!

The original preparers of trig and similar tables put a lot of thought into how to minimize computational effort. These days, if you had to prepare a TABLE, you would probably just use a computer to integrate a differential equation with a method to give the required accuracy and a step size consistent with the design of the table. A pair of simple first order (single) constant coefficient ODEs would be just right for sines and cosines.

Bill

Where upon I then asked where and why you disagree (which means 'did not agree') with Don Kelly. Again, not a difficult question. Instead hob goes into some kind of tirade about reading his original (and confusing) first post.

Ok, hob. You don't completely agree with Don Kelly. Now tell us what you don't agree with. Still no reason for an emotional outburst especially when the question is so easy to answer. What part of Don Kelly's post do you not agree with ... and why?

Either you post in agreement with Don Kelly or you have some disagreement with his post. Which is it? If your post did not agree with his, then what is it in his post you don't agree upon? Again, a simple question that only requires a simple answer.