I have decided trigonometry will be one of my first topics. I have done quite a lot of trigonometry at my high school level (in India, that is equivalent to college in many other countries). Further, I have studied hyperbolic functions during my first semester in college. That covers a major portion of the topic. But still, I want my lecture to be complete. Is there a text which covers trigonometry completely? I have S.L. Loney, but sometimes I feel that book might be outdated. Is there a newer text which records the new developments and applications of trigonometry? Thanks in advance.
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1Not quite an answer, but there most certainly should be a Schaums outline for Trig that would give you an expansive list of things you could cover. Moreover, they are very cheap. – mathematics2x2life Apr 26 '20 at 08:09
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2@mathematics2x2life How an "expansive list" can be "very cheap" ? :) :):) – Jean Marie Apr 26 '20 at 08:50
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1Of possible use: Good book on advanced trig (and this) AND Is there a “rigorous” book on “complete” trigonometry? AND Éléments de Trigonométrie Plane et Sphérique (copy at google-books) by Émile Gelin (the most complete trig book I know of) AND my philosophy of the unit circle. – Dave L. Renfro Apr 26 '20 at 13:27
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1Also, there is a HUGE amount of little-known but relevant 1800s literature freely available on the internet. For example, see the many references in my answer to Evaluate $\lim_{x\to 0}\frac{x-\sin x}{x\sin x}$ Without L'Hopital. As for "a newer text which records the new developments and applications of trigonometry", I think the only thing you'll find that's both nontrivial (compared to the older classics, some of which are in my previous comment) and recent will be in math contest problem books. – Dave L. Renfro Apr 26 '20 at 13:39
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1For hyperbolic functions, see this 8 October 2009 sci.math essay on the Gudermannian function AND ... the early drama of the hyperbolic functions by Janet Heine Barnett AND A Treatise on Plane Trigonometry, Containing an Account of Hyperbolic Functions by John Casey AND Hyperbolic Functions by James McMahon. – Dave L. Renfro Apr 26 '20 at 13:59
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1You need to be careful with old trigonometry books, because a lot of the content is focused on solving triangles in ways that will avoid large errors due to rounding, use log tables efficiently, minimize hand computations, etc. For most students, this is excessive now that calculators are widely available. – Anonymous May 27 '20 at 02:42