Talk:Trigonometric functions: Difference between revisions

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== Algebraic value of sin 45° ==

{{ping|DVdm‬}} reverted my change from

:<math>\sin \frac\pi4 = \sin 45^\circ = \frac{\sqrt{2}}{2} = \frac{\sqrt2}2</math>

to

:<math>\sin \frac\pi4 = \sin 45^\circ = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt2}</math>

with the comment "Sqrt(2)/2 is much more common than 1/sqrt(2) in the literature". Though I understand that &radic;2/2 is more common, the line gives it twice. I wonder if it may help learners to know that both expressions are valid, should they come across the rarer form. Does anyone have any thoughts on this?

Cheers,<br />'''[[User:cmglee|cm&#610;&#671;ee]]'''&#9094;[[User_Talk:cmglee|&#964;a&#671;&#954;]] 22:55, 5 July 2020 (UTC)

:{{u|Crissov}} added the accidentally duplicate values on [[Special:Diff/937238790|23 January 2020]]. Previously, the values looked [[Special:PermanentLink/937232343#Algebraic values|like this]] and the duplication probably came from the "easy way to remember" values. Probably best to omit. [[User:Johnuniq|Johnuniq]] ([[User talk:Johnuniq|talk]]) 23:57, 5 July 2020 (UTC)

::Yes, I already removed the duplicate values: [https://en.wikipedia.org/w/index.php?title=Trigonometric_functions&type=revision&diff=966142213&oldid=966141888]. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 06:33, 6 July 2020 (UTC)

:::It might make sense to add a note to show it either way [[User:Bera678|Bera678]] ([[User talk:Bera678|talk]]) 12:42, 17 December 2023 (UTC)

== Notes and References ==

Line 166 ⟶ 149:

: tau is fringe, so doesn't belong here. [[User:Tito Omburo|Tito Omburo]] ([[User talk:Tito Omburo|talk]]) 11:06, 14 March 2025 (UTC)

:IMHO, {{mvar|𝜏}} is interesting but not common enough in use for use in this article. —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 12:50, 14 March 2025 (UTC)

::Ok, fair enough [[User:TheGrifter80|TheGrifter80]] ([[User talk:TheGrifter80|talk]]) 09:36, 15 March 2025 (UTC)

== Degree sign explicitly shown ==

In the [[Trigonometric functions#Radians versus degrees|Radians versus degrees]] section, it says: "If units of degrees are intended, the degree sign must be explicitly shown (sin x°, cos x°, etc.)." I don't think this makes any sense. Extracting the unit out of a variable (i.e. making the variable a dimensionless scalar) is discouraged pretty much everywhere, as far as I'm aware. (In this case the degree is not really even a unit but more like a constant, which makes this even worse.) I'm going to remove the passage. [[User:Granite11|Granite11]] ([[User talk:Granite11|talk]]) 20:11, 1 July 2025 (UTC)

:Let's discuss this first before editing. —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 20:15, 1 July 2025 (UTC)

:I think of the degree sign not as a {{!tq|unit}} but as a {{tq|multiplicative factor}}, with the value {{math|''π''/180}}. That is, much as {{math|90''x''}} means {{math|90}} times whatever value {{mvar|x}} has, an expression like {{math|90°}} means {{math|90}} times {{math|''π''/180}}, which is {{math|''π''/2}}, and is thus converted to radians before being handed to a trigonometric function. —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 20:20, 1 July 2025 (UTC)

::I just published my changes before reading your reply—sorry about that. I think all of the text I removed was either redundant, or in the case of the claim that a degree sign must be suffixed to the variable symbol, sketchy. I agree completely with your view of the degree as a multiplicative factor, and the last sentence of the section mentions that still. [[User:Granite11|Granite11]] ([[User talk:Granite11|talk]]) 21:59, 1 July 2025 (UTC)

:This doesn't make sense to me either. I would never write {{tmath|\cos x^\circ}}, and can't remember having ever seen that notation. It's just {{tmath|\cos x}}, even if {{tmath|x}} is an angle that has been specified in degrees.

:What is fair to say is that someone should try not to write {{tmath|\cos 60}} when they mean {{tmath|\cos 60^\circ}}, because the former is potentially confusing. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 03:04, 2 July 2025 (UTC)

:: For what it's worth, in mathematica the degree symbol is a constant numerical factor. This is potentially a source for this sometimes being the case. [[User:Tito Omburo|Tito Omburo]] ([[User talk:Tito Omburo|talk]]) 11:58, 2 July 2025 (UTC)