Powers of trigonometric functions - Revision history

Christian Lawson-Perfect at 14:50, 6 July 2021

2021-07-06T14:50:07Z

← Older revision		Revision as of 15:50, 6 July 2021
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	\[ y = f^{-1}(x) \implies x = f(y) \]		\[ y = f^{-1}(x) \implies x = f(y) \]

	In his entry on Notation in the Edinburgh Encyclopedia <ref>The Edinburgh Encyclopedia, 1830, pp. 398-399. [https://babel.hathitrust.org/cgi/pt?id=chi.21708663&view=1up&seq=431 Copy on HathiTrust]</ref>, Charles Babbage is scathing about this convention.		In his entry on Notation in the Edinburgh Encyclopedia <ref>The Edinburgh Encyclopedia, 1830, pp. 398-399. [https://babel.hathitrust.org/cgi/pt?id=chi.21708663&view=1up&seq=431 Copy on HathiTrust]. [https://www.maths.ed.ac.uk/~csangwin/Babbage1830.pdf Transcribed copy].</ref>, Charles Babbage is scathing about this convention.

	<blockquote>Although a definition can not be false, it may be improper.</blockquote>		<blockquote>Although a definition can not be false, it may be improper.</blockquote>

SparksMaths at 12:11, 2 July 2021

2021-07-02T12:11:56Z

← Older revision		Revision as of 13:11, 2 July 2021
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	[[Category:Inconsistencies]]		[[Category:Inconsistencies]]
	[[Category:Unpleasantness]]		[[Category:Unpleasantness]]
	[[Category:Conflicting ~~Definitions~~]]		[[Category:Conflicting definitions]]

	When writing a power of a trigonometric function or logarithm, it's common to write the power as a superscript before the brackets:		When writing a power of a trigonometric function or logarithm, it's common to write the power as a superscript before the brackets:

SparksMaths at 12:10, 2 July 2021

2021-07-02T12:10:35Z

← Older revision		Revision as of 13:10, 2 July 2021
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	[[Category:Inconsistencies]]		[[Category:Inconsistencies]]
	[[Category:Unpleasantness]]		[[Category:Unpleasantness]]
			[[Category:Conflicting Definitions]]

	When writing a power of a trigonometric function or logarithm, it's common to write the power as a superscript before the brackets:		When writing a power of a trigonometric function or logarithm, it's common to write the power as a superscript before the brackets:

SparksMaths: Added discussion of inverse trig functions and their index notation

2021-07-02T12:07:49Z

Added discussion of inverse trig functions and their index notation

← Older revision		Revision as of 13:07, 2 July 2021
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	<blockquote>Although a definition can not be false, it may be improper.</blockquote>		<blockquote>Although a definition can not be false, it may be improper.</blockquote>

			Further aggravating this issue is the commonplace use of conventional function notation to denote the inverse of trigonometric functions. When used alongside the \(\sin^2(x)\) notation this juxtaposes the contradictory notation quite sharply, and may cause potential confusion for learners. For example:

			\[\sin^2(x) = (\sin(x))^2 \] (index notation, as in the original example)

			but
			\[ \sin^{-1}(x) \neq \frac{1}{\sin(x)}\]
			rather
			\[ \sin^{-1}(x) = \arcsin(x) \] (function notation)

			It is arguable that conventions such as \(\arcsin(x)\) for inverse sine, and \(\csc(x)\) for the reciprocal of sine (or often \(\textrm{cosec}(x)\) - at least in UK schools), are better used to avoid these notational contradictions.

	==References==		==References==

	<references/>		<references/>

David Eppstein: or log

2021-06-30T17:44:06Z

or log

← Older revision		Revision as of 18:44, 30 June 2021
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	[[Category:Unpleasantness]]		[[Category:Unpleasantness]]

	When writing a power of a trigonometric function, it's common to write the power as a superscript before the brackets:		When writing a power of a trigonometric function or logarithm, it's common to write the power as a superscript before the brackets:

	\[ \sin^2(x) = (\sin(x))^2 \]		\[ \sin^2(x) = (\sin(x))^2 \]

Christian Lawson-Perfect at 10:22, 30 June 2021

2021-06-30T10:22:13Z

← Older revision		Revision as of 11:22, 30 June 2021
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	<blockquote>Although a definition can not be false, it may be improper.</blockquote>		<blockquote>Although a definition can not be false, it may be improper.</blockquote>

			==References==

	<references/>		<references/>

Christian Lawson-Perfect: Created page with "Category:Ambiguities Category:Inconsistencies Category:Unpleasantness When writing a power of a trigonometric function, it's common to write the power as a supers..."

2021-06-30T10:21:46Z

Created page with "Category:Ambiguities Category:Inconsistencies Category:Unpleasantness When writing a power of a trigonometric function, it's common to write the power as a supers..."

New page

[[Category:Ambiguities]]
[[Category:Inconsistencies]]
[[Category:Unpleasantness]]

When writing a power of a trigonometric function, it's common to write the power as a superscript before the brackets:

\[ \sin^2(x) = (\sin(x))^2 \]

This conflicts with the conventional notation for inverses and repeated application of functions:

\[ f^2(x) = f(f(x)) \]

\[ y = f^{-1}(x) \implies x = f(y) \]

In his entry on Notation in the Edinburgh Encyclopedia <ref>The Edinburgh Encyclopedia, 1830, pp. 398-399. [https://babel.hathitrust.org/cgi/pt?id=chi.21708663&view=1up&seq=431 Copy on HathiTrust]</ref>, Charles Babbage is scathing about this convention.

<blockquote>Although a definition can not be false, it may be improper.</blockquote>

<references/>