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:::Several parts of this article might benefit from a substantial rewrite, but trying to cut out random words from its sentences doesn't seem that helpful. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 15:31, 29 September 2024 (UTC)
::::What parts of the article should be rewritten, and how? Also, what do you mean by “random words”? Also, in the expression “Trigonometric function sin θ”, would you agree that “Trigonometric function” is redundant, at least in said caption? [[User:Solomonfromfinland|Solomonfromfinland]] ([[User talk:Solomonfromfinland|talk]]) 15:36, 29 September 2024 (UTC)
:::::For example, some subsections of {{alink|Definitions in analysis}} are too long and belabor the details. The section about {{alink|Radians versus degrees}} is too long and is distracting at this length near the top. The historical definition used for 2000 years between the 2nd century BC and at least the end of the 18th century, of "trigonometric lines" representing line segments with respect to a circular arc, is not discussed at all and is only mentioned in a half sentence. There is one sentence about "The sine and cosine functions are one-dimensional projections of uniform circular motion" but this should be a whole section. There is no discussion of the relation of trigonometric functions to vectors, but this should also be a whole section. There is one example of a Fourier series, but this should again be a whole section. The section {{alink| In the complex plane}} should be moved to top level and substantially expanded. The history section mentions "Historically, trigonometric functions were often combined with logarithms in compound functions like the logarithmic sine, ...", but this topic should again be a whole section (and ideally link to a main article which would discuss the topic in detail, since no Wikipedia article currently does). There should be a whole section about the relation between circular and hyperbolic functions, but currently the latter are barely mentioned here. The {{alink|Applications}} section is a mess in my opinion: the material currently there is basic tools of trigonometry and should be moved to separate top-level sections, but we don't mention any of the applications of trigonometry (historically astronomy, navigation, surveying, architecture, gunnery, ..., or more recently nearly every part of science and engineering).
:::::Anyway as for your specific questions: The sentences about similar triangles should be more substantially rewritten for clarity. I don't think your proposed changes are much better than what was there. {{tq|i=yes|"long gap between the table"}} – the images to the right there are not great and could probably be usefully moved or replaced, and the table's content also doesn't match the section, and it should be moved or modified. Shortening the captions doesn't really make a significant improvement in my opinion. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 17:13, 29 September 2024 (UTC)
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