编辑

Question 1

您应该使用语义标记来标记文档元素，而不是手动格式化。例如，如果Trigon...是文档的标题，则您希望

\title{Trigonometric Functions Evaluated at Negative Angles}% if it is the title of the document
\author{}\date{}
\maketitle

或者如果它是某个部分的标题，你需要

\section{Trigonometric Functions Evaluated at Negative Angles}% if it is a section heading

或者如果该部分不应编号，则使用

\section*{Trigonometric Functions Evaluated at Negative Angles}% if it is an unnumbered section heading

类似的观点适用于定义等。您需要配置您的文档，以便您可以说，例如

\begin{definition}{something}
  This is a definition of something.
\end{definition}

并让此代码产生您想要的格式。

amsthm和等软件包ntheorem可以帮助您轻松完成此操作。

这可确保格式一致，并且可以通过改变序言中的几个选项轻松更改所有定义或所有词条的格式。

没有环境centering。\centering是一个命令。

\begin{center}
  Something centred with vertical spacing before and after.
\end{center}
{\centering Something centred without additional vertical spacing.\par}

amsthm这是一个完整的示例，它使用(via )提供的功能amsart来配置definition环境，并使用常规\newenvironment来创建trig环境。语法如下definition：

\begin{definition}
  Definition of something.
\end{defintion}

并且对于trig：

\begin{trig}{Heading}
  Whatever.
\end{trig}

代码：

\documentclass{amsart}
\usepackage{titling}
\pretitle{\begin{center}\Large\bfseries}
\posttitle{\par\end{center}\vskip 0.5em}
\newtheoremstyle{mytheorem}{2.5mm}{2.5mm}{\itshape}{0pt}{\bfseries}{}{\newline}{#1}
\theoremstyle{mytheorem}
\newtheorem{definition}{Definition}
\newenvironment{trig}[1]{%
  \vskip 2.5mm plus .2ex minus 1ex\par
  \noindent\textbf{#1}\par\noindent
  \itshape\ignorespaces}{}
\begin{document}
\title{Trigonometric Functions Evaluated at Negative Angles}
\author{}\date{}
\maketitle

\begin{definition}
  $\overline{OA}$ and $\overline{OB}$ are the initial and terminal sides of $\angle{AOB}$, respectively, ${\mathrm{m}}\angle{AOB} = \theta$, and $0 \leq \theta < 360^{\circ}$. If $\overline{OB^{\prime}}$ is the reflection of $\overline{OB}$ across the line containing $\overline{OA}$, ${\mathrm{m}}\angle{AOB^{\prime}} = -\theta$.
\end{definition}

\begin{trig}{Trigonometric Identities}
  For any real number $0 < \theta \leq 360$,
    \begin{equation*}
      \cos(-\theta) = \cos\theta
      \qquad \mbox{\em{and}} \qquad
      \sin(-\theta) = -\sin\theta
    \end{equation*}
    and so, for any such $\theta$ distinct from $90^{\circ}$ and $270^{\circ}$,
    \begin{equation*}
      \tan(-\theta) = -\tan\theta .
    \end{equation*}
\end{trig}    
\end{document}

编辑

在评论中，您表示您真正想要的是实现符合 AMS 风格的目标。如果是这样，那么您应该查看AMSamsart-template.tex类的文档。amsart.cls提供了三种定理样式：theorem和。该模板包含一些示例定理定义，进一步的定义应使用标准样式。remarkplain

例如：

\documentclass{amsart}
% to use standard AMS formatting, take code from amsart-template.textbf
% if appropriate, your document body should also reflect the structure of that template and follow the guidance provided in the comments there and the documentation
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{xca}[theorem]{Exercise}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
\numberwithin{equation}{section}
% some additions to demonstrate the third style provided by amsart
\theoremstyle{plain}
\newtheorem{comment}[theorem]{Comment}
\begin{document}
\title{Trigonometric Functions Evaluated at Negative Angles}
\author{}\date{}
\maketitle

\section{Introduction}

\begin{definition}
  $\overline{OA}$ and $\overline{OB}$ are the initial and terminal sides of $\angle{AOB}$, respectively, ${\mathrm{m}}\angle{AOB} = \theta$, and $0 \leq \theta < 360^{\circ}$. If $\overline{OB^{\prime}}$ is the reflection of $\overline{OB}$ across the line containing $\overline{OA}$, ${\mathrm{m}}\angle{AOB^{\prime}} = -\theta$.
\end{definition}

\begin{definition}[something]
  This is a definition of `something'.
\end{definition}

\begin{remark}
  This is a remark.
\end{remark}

\begin{remark}[Aardvarks]
  This is a remark about aardvarks.
\end{remark}

\begin{comment}[Trigonometric Identities]
  For any real number $0 < \theta \leq 360$,
    \begin{equation*}
      \cos(-\theta) = \cos\theta
      \qquad \mbox{\em{and}} \qquad
      \sin(-\theta) = -\sin\theta
    \end{equation*}
    and so, for any such $\theta$ distinct from $90^{\circ}$ and $270^{\circ}$,
    \begin{equation*}
      \tan(-\theta) = -\tan\theta .
    \end{equation*}
\end{comment}

\end{document}

Answer