What is recommendations for the best books of trigonometry contain material about versine, coversine and other trigonometric functions that are rarely used, basic trigonometry, and concept about deriving Trigonometry identities?
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3I don't know whether any book published since 1900 has anything to say about the versine and coversine. – Gerry Myerson Jun 06 '19 at 13:13
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2You could look up the so-called haversine formula for distance on a sphere. That formula is still used today, though usually with the haversine translated into something involving the sine function (since computer math libraries usually don’t implement haversine directly). – David K Jun 07 '19 at 01:57
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There is one recent example I have seen that briefly treats the versed sine function, $\operatorname{vers} x$, and its inverse, $\operatorname{vers}^{-1} x$, as an exercise. See pages 167 and 168 of:
How to Integrate It: A practical guide to finding elementary integrals by S. Stewart (Cambridge University Press, 2018)
Here the derivatives of the $\operatorname{vers} x$ and $\operatorname{vers}^{-1} x$ are found, the indefinite integral that leads to $\operatorname{vers}^{-1} x$ considered, and $\operatorname{vers}^{-1} x$ expressed in terms of the inverse cosine function presented. Not much I know, but you may find it a helpful start.
omegadot
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even though this is not what I mean, but you've shown a good book about integrals. Thanks ^ – user516076 Jun 07 '19 at 02:04
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The actual title is, of course, How to Integrate It. https://www.cambridge.org/core/books/how-to-integrate-it/6030DFD3F3E36C296DDAD3228478FD25 – Gerry Myerson Jun 08 '19 at 04:07
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