mom2bee Posted November 6, 2014 Share Posted November 6, 2014 I know that this is probably a dumb question but...How exactly do you use the tables in the back of math books. Like the log and trig values? I bought a copy of Algebra and Trigonometry: Structure and Method (new edition) Book 2 © 1982 and it includes Trigonometric tables. I feel stupid to ask but...Do you keep the work in exact form until the end and then sub in the value and do the arithmetic at the very end? If so, was this typically done by hand or did people use pocket calculators for that final step? Quote Link to comment Share on other sites More sharing options...
kiana Posted November 6, 2014 Share Posted November 6, 2014 Yes, you sub it in at the final step. People did not use pocket calculators because they were expensive. They'd use a slide rule or do it by hand. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 6, 2014 Share Posted November 6, 2014 Yep, no calculators. For "nice" angles, you'd memorize the values of the trig functions - for arbitrary angles, you'd look the m up in the table very last thing. You can't do trig with a slide rule. In school, we had to use tables to find square roots and cube roots and logarithms and exponentials. We used calculators for the first time in 10th grade, in 1983/84. The calculator that was required cost 10% of an average monthly wage in our country. Quote Link to comment Share on other sites More sharing options...
mom2bee Posted November 6, 2014 Author Share Posted November 6, 2014 Oh, okay but here's a question...how did they generate those trig and log tables to begin with??? I know that seems like a goofy question, but I'm serious... Quote Link to comment Share on other sites More sharing options...
mom2bee Posted November 6, 2014 Author Share Posted November 6, 2014 Also, how did the slide rule develop? The abacus is obvious, but a slide rule just seems so....wow? I can't fathom how they came up with it. Quote Link to comment Share on other sites More sharing options...
kiana Posted November 6, 2014 Share Posted November 6, 2014 Painstaking calculation. Here's a website with an explanation (which is typeset much better than can be set here). http://www.clarku.edu/~djoyce/trig/compute.html ETA: Biography of the guy who came up with the slide rule (shortly after Napier came up with logarithms): http://en.wikipedia.org/wiki/William_Oughtred Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 6, 2014 Share Posted November 6, 2014 Oh, okay but here's a question...how did they generate those trig and log tables to begin with??? I know that seems like a goofy question, but I'm serious... I am not entirely sure. You can, of course, easily obtain a value for the trig functions from geometry - you could do a precision drawing, measure and calculate your ratios of your sides. Alternatively one could have summed up the series expansion. And then, you can of course use trig identities to find more values. The calculator has to do the calculation internally as well; if I am not mistaken, the calculator sums up the series. Quote Link to comment Share on other sites More sharing options...
Muttichen Posted November 7, 2014 Share Posted November 7, 2014 Wait -- do new math books not have trig and log tables?????? My dh has a PhD in math and he always made our kids start out using the tables so they'd have an understanding of how the numbers work instead of them just magically appearing when you press a button on the calculator. That way they will know if they get an unreasonable answer. Once they understood it all well, he'd let them use the calculator. Quote Link to comment Share on other sites More sharing options...
kiana Posted November 7, 2014 Share Posted November 7, 2014 Wait -- do new math books not have trig and log tables?????? My dh has a PhD in math and he always made our kids start out using the tables so they'd have an understanding of how the numbers work instead of them just magically appearing when you press a button on the calculator. That way they will know if they get an unreasonable answer. Once they understood it all well, he'd let them use the calculator. They do not. I'm not sure exactly when they stopped being included, but sometimes in the '90s seems about right. My precalc textbook published in the late '80s still had them included, but I haven't seen a new edition with tables in them in years. Quote Link to comment Share on other sites More sharing options...
Jann in TX Posted November 7, 2014 Share Posted November 7, 2014 I took Pre-Calc in 1982... Yes, we did have basic scientific calculators (required for the course)--- mine was a TI and cost $35. (I met my DH in that class...) We used the tables as well-- but the calculators were more accurate and were COMMON at the time. Those calculators did not solve the problem for you (like some graphing calculators can). We had to show all of our work and could use the calculator in the filnal step-- even when we used tables. I liked using the tables for basic Trig-- I think it helped me to see the relationships between angle size (complements/supplements) and sin/cos ratios. When we got to the more advanced Trig problems I was more than happy to use the calculator. -- When I teach radicals to Algebra 1, Geometry and Algebra 2 students I teach them to make their own tables-- MUCH easier to use than calculators when reducing radicals! Quote Link to comment Share on other sites More sharing options...
Space station Posted November 7, 2014 Share Posted November 7, 2014 TOPS has a unit called Far Out Math that is designed to show how slide rules work. You make your own paper one and then use it. Quote Link to comment Share on other sites More sharing options...
Tsuga Posted November 8, 2014 Share Posted November 8, 2014 Painstaking calculation. Here's a website with an explanation (which is typeset much better than can be set here). http://www.clarku.edu/~djoyce/trig/compute.html ETA: Biography of the guy who came up with the slide rule (shortly after Napier came up with logarithms): http://en.wikipedia.org/wiki/William_Oughtred When I was in school, a million years ago in 1994, we had to calculate all of those ourselves... Every time. I was literally in the very last class at my university--the absolute last--taught by a legacy substitute prof, a wonderful woman--who didn't know how to use a scientific calculator. So we were the very last ones to take our calculus tests without a calculator. :) I think it helped me on the GRE. Quote Link to comment Share on other sites More sharing options...
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