[Tex/LaTex] Trigonometric notation with Initial capital Letter and Italic

capitalizationitalic

How can we make First letter Capital while using trigonometric functions.
eg: \cos (60^\circ) gives simple cos (all in small). What is needed is 'Cos' (with initial capital).
For italics in mactex i used \it but it didn't italicized 'cos' only the number '60'. So how to do that?

Best Answer

I would highly recommend you not do this, but you can use \DeclareMathOperator to change how the operators are typeset:

\DeclareMathOperator{\cos}{Cos}
\DeclareMathOperator{\sin}{Sin}

enter image description here

If you want the operator name in italics you can instead use:

\DeclareMathOperator{\cos}{\mathit{Cos}}
\DeclareMathOperator{\sin}{\mathit{Sin}}

enter image description here

Again, I would advice you to not do this. It is not consistent with the normal conventions.

Notes:

The \let were necessary as we are redefining existing macros, so \let the existing definition to \relax eliminates the error message.

Code:

\documentclass{article}
\usepackage{amsmath}

\let\cos\relax
\let\sin\relax
\DeclareMathOperator{\cos}{Cos}
\DeclareMathOperator{\sin}{Sin}

\begin{document}
$\cos^2 \theta + \sin^2 \theta = 1$
\end{document}

Related Solutions

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\addcontentsline{toc}{chapter}{\protect\numberline{\thechapter}#1}

and

\addcontentsline{toc}{chapter}{#1}

should read with \MakeUppercase{#1} instead of #1.

[Tex/LaTex] Command to uppercase the first letter of a maths command

Not quite a generic solution, as it assumes that the first letter is unique in the operator name. The \relax are perhaps a bit optional I am always confused about when I should put some or not ;-)

\documentclass{amsart}
\usepackage[english,spanish]{babel}
\makeatletter
\newcommand\Max{\@tempcnta=\mathcode`\m\relax
\mathcode`\m=\mathcode`\M\max\mathcode`\m=\@tempcnta\relax}
\makeatother

\begin{document}
  \begin{equation*}
    \max_0^\infty = \Max_0^\infty \Max\nolimits_0^\infty m M 
  \end{equation*}
\selectlanguage{english}
  \begin{equation*}
    \max_0^\infty = \Max_0^\infty \Max\nolimits_0^\infty m M
  \end{equation*}
\end{document}

Thanks to egreg for his comment(s). After having temporarily incorporated his simplification (of the code of my initial proposal) to the extension I am now proposing, I now return to the original thing, but also incorporate the later improvements signaled by egreg.

The same restriction as above applies (the operator name should contain its initial letter only once).

\documentclass{amsart}
\usepackage[english,spanish]{babel}
\pagestyle{empty}

\makeatletter

\def\Tr@nsmogrify#1#2.{\expandafter\newcommand\csname #1#2\endcsname
{\mathchardef\Tr@ns@temp=\mathcode\lccode`#1\relax
\mathcode\lccode`#1=\mathcode`#1\lowercase{\csname#1#2\endcsname}%
\mathcode\lccode`#1=\Tr@ns@temp\relax}}

\@for\x:=Sin,Cos,Max,Min,Lim,Limsup,Liminf,Inf\do{%
\expandafter\Tr@nsmogrify \x.}

\makeatother

\begin{document}

\thispagestyle{empty}
\noindent
\begin{minipage}{.5\linewidth}
  \begin{align*}
\min_0^\infty &= \Min_0^\infty\\
\min\nolimits_0^\infty &= \Min\nolimits_0^\infty\\
\max_0^\infty &= \Max_0^\infty\\
\lim_{x\to\infty} &= \Lim_{x\to\infty}\\
\liminf_{x\to\infty} &= \Liminf_{x\to\infty}\\
\limsup_{x\to\infty} &= \Limsup_{x\to\infty}\\
\inf_{x\in A} &= \Inf_{x\in A}\\
\sin^2 x +\cos^2 x  &= \Sin^2 x +\Cos^2 x \\
\limsup_{x\to\infty} &= \Limsup_{x\to\infty}\\
m,M,l,L&,s,S,c,C
  \end{align*}
\end{minipage}
\begin{minipage}{.5\linewidth}
\selectlanguage{english}%
  \begin{align*}
\min_0^\infty &= \Min_0^\infty\\
\min\nolimits_0^\infty &= \Min\nolimits_0^\infty\\
\max_0^\infty &= \Max_0^\infty\\
\lim_{x\to\infty} &= \Lim_{x\to\infty}\\
\liminf_{x\to\infty} &= \Liminf_{x\to\infty}\\
\limsup_{x\to\infty} &= \Limsup_{x\to\infty}\\
\inf_{x\in A} &= \Inf_{x\in A}\\
\sin^2 x +\cos^2 x  &= \Sin^2 x +\Cos^2 x \\
\limsup_{x\to\infty} &= \Limsup_{x\to\infty}\\
m,M,l,L&,s,S,c,C
  \end{align*}
\end{minipage}
\end{document}

Here is the result:

PNG image with english and spanish operators with first letter made uppercase

Addendum:

The above definitions make \Xyzt behave like \xyzt with respect to the positions of limits, in inline as well as display style. But there is a difference: \[\sin\limits_a^b\] or $\sin\limits_a^b$ do not put the a and b in limits positions, whereas \[\Sin\limits_a^b\] and $\Sin\limits_a^b$ do. I would call this an unintended feature rather than a bug! This is illustrated by the following:

different behaviors of limits

Note the asymmetry of behavior of the amsmath operators \sin and \min. Whereas for the first \limits does nothing, for the second \nolimits does work. I will not qualify this as a bug of amsmath (or rather amsopn.sty), as there must be reasons beyond me, but I had never realized that until now.

PS: obviously the above image comes from a source with \usepackage[spanish]{babel} but I checked that the exact same behavior is observed without any loading of babel. Note also that \sin and \min in amsopn.sty are not defined via \DeclareMathOperator, respectively \DeclareMathOperator*, but only by some part of the code of these macros, but this is another not relevant detail.

PS2: as a matter of fact the [spanish]{babel} defined operator names behave differently from the analogous amsmath provided names with respect to limits.

$examples of operator names with \limits$