我正在嘗試繪製函數 y=4/pi * arccos(x/4) 和 2-sqrt(x) （見圖）。這來自美聯社中心。我無法確定用於顯示這兩個圖像的正確軸。我可以毫無問題地繪製平方根函數，但嘗試添加反三角函數卻讓我很困惑。
任何幫助，將不勝感激。我嘗試用谷歌搜尋它，但運氣不佳。
\documentclass[11pt,letterpaper]{article}
\usepackage[utf8]{inputenc}
\usepackage{adjustbox}
\usepackage{fullpage}
\usepackage[top=2cm, bottom=4.5cm, left=2.5cm, right=2.5cm]{geometry}
\usepackage{amsmath,amsthm,amsfonts,amssymb,amscd}
\usepackage{multicol}
\usepackage{enumerate}
\usepackage{fancyhdr}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{amssymb}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{plotmarks}
\usetikzlibrary{arrows}
\usetikzlibrary{shapes.misc, positioning}
\usetikzlibrary{arrows,shapes,positioning,snakes}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{arrows.meta,bending}
\tikzset{font=\footnotesize}
\setlength{\parindent}{0.0in}
\setlength{\parskip}{0.05in}
\newcommand*{\dprime}{^{\prime\prime}\mkern-1.2mu}
\newcommand*{\trprime}{^{\prime\prime\prime}\mkern-1.2mu}
% Edit these as appropriate
\newcommand\course{AP Calculus AB}
\pagestyle{fancy}
\headheight 35pt
\lhead{Mark Sparks}
\chead{\textbf{Topic 8.5 Finding the Area Between Curves \\ Expressed as Functions of \(x\) }}
\rhead{\course \\ \today}
\lfoot{Mr. Bennett}
\cfoot{Flint Hill Upper School}
\rfoot{\small\thepage}
\headsep 1.5em
\renewcommand{\baselinestretch}{1.5}
\renewcommand{\arraystretch}{1.5}
\begin{document}
\subsection*{AP Test Preparation}
\begin{center}
\begin{tikzpicture}[scale=.75]
\begin{axis}[thick,
scale only axis,
grid=major,
axis lines=middle,
inner axis line style={-Triangle},
ytick={-1,0,...,3},
xtick={-1,0,...,5},
ymin=-1,
ymax=3,
xmin=-1,
xmax=5,
]
\addplot[thick,samples=1000,domain=0:4]{2-sqrt(x)};
\addplot[thick,samples=1000,domain=0:4]{1.27324*acos(x/4)
\node at (2,1){\(R\)};
\end{axis}
\end{tikzpicture}
\end{center}
\begin{enumerate}
\item Let \(R\) be the region in the first quadrant bounded above by the graph of \(y=\dfrac{4}{\pi}\cos^{-1}\left(\dfrac{x}{4}\right)\) and below by the graph of \(y=2-\sqrt{x}\), as shown in the figure above. What is the area of the region?
A. \(\dfrac{4}{3}\) \\
B. \(\dfrac{16}{\pi}+\dfrac{8}{3}\) \\
C. \(\dfrac{16}{\pi}-\dfrac{8}{3}\) \\
D. \(\dfrac{16}{3}\) \\
\rule{\textwidth}{.5pt}
\end{enumerate}
\end{document}
答案1
我你的程式碼有兩個錯誤。
首先，\addplot[thick,samples=1000,domain=0:4]{1.27324*acos(x/4)您錯過了閉括號和半柱};。
其次，acos函數傳回度數結果。因此 acos(0) 傳回 90。就像 (4/pi) * acos(x) 一樣，(pi/180) * (4/pi) 是 1/45 （約 0.02222），所以，只需替換
\addplot[thick,samples=1000,domain=0:4]{1.27324*acos(x/4)
經過
\addplot[thick,samples=1000,domain=0:4]{0.02222*acos(x/4)};
你得到：
