From ef086cc3b3a384b99793dbecdaf7360895701b09 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Tue, 16 Jan 2024 21:26:05 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E9=AB=98=E4=B8=80=E4=B8=8B?= =?UTF-8?q?=E8=8B=A5=E5=B9=B2=E5=9F=BA=E7=A1=80=E7=9F=A5=E8=AF=86=E6=A2=B3?= =?UTF-8?q?=E7=90=86?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/BasicKnowledge.json | 219 ++++++++++++++++++++++++++++++++++++ 1 file changed, 219 insertions(+) diff --git a/题库0.3/BasicKnowledge.json b/题库0.3/BasicKnowledge.json index f7f6f8bd..7a3816ee 100644 --- a/题库0.3/BasicKnowledge.json +++ b/题库0.3/BasicKnowledge.json @@ -1063,5 +1063,224 @@ "K0314002B" ], "content": "正弦定理: \\blank{50}$=$\\blank{50}$=$\\blank{50}." + }, + "B00149": { + "lesson": "K0315", + "objs": [ + "K0315001B", + "K0315002B" + ], + "content": "余弦定理: $a^2=$\\blank{100}; $b^2=$\\blank{100}; $c^2=$\\blank{100}." + }, + "B00150": { + "lesson": "K0315", + "objs": [ + "K0315001B", + "K0315002B" + ], + "content": "余弦定理变形: $\\cos A=$\\blank{50}; $\\cos B=$\\blank{50}; $\\cos C=$\\blank{50}." + }, + "B00151": { + "lesson": "K0316", + "objs": [ + "K0308003B" + ], + "content": "已知 $a \\in[0,1]$, $\\arcsin a$ 表示\\blank{100}." + }, + "B00152": { + "lesson": "K0316", + "objs": [ + "K0308003B" + ], + "content": "已知 $a \\in[0,1]$, $\\arccos a$ 表示\\blank{100}." + }, + "B00153": { + "lesson": "K0316", + "objs": [ + "K0308003B" + ], + "content": "已知 $a \\in[0,+\\infty)$, $\\arctan a$ 表示\\blank{100}." + }, + "B00154": { + "lesson": "K0317", + "objs": [ + "K0317002B" + ], + "content": "测量问题中的有关名词和方位表示, 如: 仰角, 俯角, 方位角等." + }, + "B00155": { + "lesson": "K0317", + "objs": [ + "K0317002B" + ], + "content": "将测量问题转化为解三角形问题后, 灵活运用正弦定理和余弦定理求解三角形." + }, + "B00156": { + "lesson": "K0318", + "objs": [ + "K0318001B" + ], + "content": "正弦函数 $y=\\sin x$ 的定义域是\\blank{50}." + }, + "B00157": { + "lesson": "K0318", + "objs": [ + "K0318002B", + "K0318003B" + ], + "content": "函数 $y=\\sin x$, $x \\in[0,2 \\pi]$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i in {-1.5,-1,-0.5,0,0.5,1,1.5}\n{\\draw [gray!50, dashed] (0,\\i) -- (7,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\foreach \\i in {0,pi/2,pi,3*pi/2,2*pi}\n{\\draw [gray!50, dashed] (\\i,-1.5) -- (\\i,1.5);};\n\\draw (pi,0) node [below] {$\\pi$};\n\\draw [->] (0,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00158": { + "lesson": "K0318", + "objs": [ + "K0318002B", + "K0318003B" + ], + "content": "函数 $y=\\sin x$, $x \\in \\mathbf{R}$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i in {-1.5,-1,-0.5,0,0.5,1,1.5}\n{\\draw [gray!50, dashed] (-7,\\i) -- (7,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\foreach \\i in {-2*pi,-3*pi/2,-pi,-pi/2,0,pi/2,pi,3*pi/2,2*pi}\n{\\draw [gray!50, dashed] (\\i,-1.5) -- (\\i,1.5);};\n\\draw (pi,0) node [below] {$\\pi$};\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00159": { + "lesson": "K0319", + "objs": [ + "K0319003B" + ], + "content": "对于函数 $y=f(x)$, 如果存在一个非零的常数 $T$, 使得当 $x$ 取其定义域 $D$ 中\\blank{50}时, 有\\blank{50}$\\in D$, 且\\blank{50}成立 ,那么函数 $y=f(x)$ 就叫做周期函数, 而这个非零常数 $T$ 就叫做函数 $y=f(x)$ 的一个周期." + }, + "B00160": { + "lesson": "K0319", + "objs": [ + "K0319002B", + "K0319003B" + ], + "content": "对于一个周期函数 $y=f(x)$, 如果在它的所有周期中存在一个\\blank{50}, 那么这个数就叫做函数 $y=f(x)$ 的最小正周期." + }, + "B00161": { + "lesson": "K0319", + "objs": [ + "K0319004B" + ], + "content": "函数 $y=\\sin x$ 的最小正周期是\\blank{50}." + }, + "B00162": { + "lesson": "K0319", + "objs": [ + "K0319005B" + ], + "content": "设 $\\omega>0$, $\\varphi \\in \\mathbf{R}$, 函数 $y=\\sin (\\omega x+\\varphi)$ 的最小正周期是\\blank{50}." + }, + "B00163": { + "lesson": "K0320", + "objs": [ + "K0320001B" + ], + "content": "正弦函数 $y=\\sin x$, $x \\in \\mathbf{R}$ 的值域是\\blank{50}." + }, + "B00164": { + "lesson": "K0320", + "objs": [ + "K0320001B" + ], + "content": "正弦函数 $y=\\sin x$, $x \\in \\mathbf{R}$ 的最大值是\\blank{50}, 此时 $x=$\\blank{50}; 最小值是\\blank{50}, 此时 $x=$\\blank{100}." + }, + "B00165": { + "lesson": "K0321", + "objs": [ + "K0321001B" + ], + "content": "正弦函数 $y=\\sin x$ 的奇偶性是\\blank{50}." + }, + "B00166": { + "lesson": "K0321", + "objs": [ + "K0321002B" + ], + "content": "正弦函数 $y=\\sin x$ 在其定义域内 (填``是''或``不是'')单调函数." + }, + "B00167": { + "lesson": "K0321", + "objs": [ + "K0321002B" + ], + "content": "正弦函数 $y=\\sin x$ 的单调增区间是\\blank{100}; 单调减区间是\\blank{100}." + }, + "B00168": { + "lesson": "K0322", + "objs": [ + "K0322001B" + ], + "content": "余弦函数 $y=\\cos x$ 的定义域是\\blank{50}." + }, + "B00169": { + "lesson": "K0322", + "objs": [ + "K0322002B" + ], + "content": "函数 $y=\\cos x$, $x \\in[0,2 \\pi]$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i in {-1.5,-1,-0.5,0,0.5,1,1.5}\n{\\draw [gray!50, dashed] (0,\\i) -- (7,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\foreach \\i in {0,pi/2,pi,3*pi/2,2*pi}\n{\\draw [gray!50, dashed] (\\i,-1.5) -- (\\i,1.5);};\n\\draw (pi,0) node [below] {$\\pi$};\n\\draw [->] (0,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00170": { + "lesson": "K0322", + "objs": [ + "K0322002B" + ], + "content": "函数 $y=\\cos x$, $x \\in \\mathbf{R}$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i in {-1.5,-1,-0.5,0,0.5,1,1.5}\n{\\draw [gray!50, dashed] (-7,\\i) -- (7,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\foreach \\i in {-2*pi,-3*pi/2,-pi,-pi/2,0,pi/2,pi,3*pi/2,2*pi}\n{\\draw [gray!50, dashed] (\\i,-1.5) -- (\\i,1.5);};\n\\draw (pi,0) node [below] {$\\pi$};\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00171": { + "lesson": "K0322", + "objs": [ + "K0322002B" + ], + "content": "余弦函数的性质:\n\\begin{center}\n\\begin{tabular}{|c|p{25em}|}\\hline 周期性 & \\\\\n\\hline 值域 & \\\\\n\\hline 最大值 & \\\\\n\\hline 最小值 & \\\\\n\\hline 奇偶性 & \\\\\n\\hline 单调增区间 & \\\\\n\\hline 单调减区间 & \\\\\n\\hline\n\\end{tabular}\n\\end{center}" + }, + "B00172": { + "lesson": "K0323", + "objs": [ + "K0323003B" + ], + "content": "``五点法''作图: 用五点法作函数 $y=A \\sin (\\omega x+\\varphi)$($A>0$, $\\omega>0$) 在一个周期内的图像时, 所取五个``关键点''的坐标为\\blank{200}." + }, + "B00173": { + "lesson": "K0323", + "objs": [ + "K0323003B" + ], + "content": "函数 $y=A \\sin (\\omega x+\\varphi)$($A>0$, $\\omega>0$) 图像变换的一般方法.\\\\\n(1) 当 $A>1$ 时,将 $y=\\sin x$ 图像上每一点的纵坐标\\blank{50}且横坐标不变; 当 $01$ 时, 将 $y=\\sin x$ 图像上每一点的横坐标\\blank{50}且纵坐标不变; 当 $0<\\omega<1$时, 将 $y=\\sin x$ 图像上每一点的横坐标\\blank{50}且纵坐标不变, 就得到 $y=\\sin \\omega x$ 的图像.\\\\\n(3) 当 $\\varphi>0$ 时, 将 $y=\\sin x$ 图像上的每一点向\\blank{50}平移\\blank{50}个单位; 当 $\\varphi<0$ 时, 将 $y=\\sin x$ 图像上的每一点向\\blank{50}平移个单位, 就得到 $y=\\sin (x+\\varphi)$ 的图像." + }, + "B00174": { + "lesson": "K0323", + "objs": [ + "K0320331B" + ], + "content": "函数 $y=A \\sin (\\omega x+\\varphi)$($A>0$, $\\omega>0$) 的振幅为\\blank{50}, 周期 $T$ 为\\blank{50}, 频率 $f$ 为\\blank{50}, 圆频率为\\blank{50}, 相位为\\blank{50}, 初始相位为\\blank{50}." + }, + "B00175": { + "lesson": "K0324", + "objs": [ + "K0324001B" + ], + "content": "正切函数 $y=\\tan x$ 的定义域是\\blank{100}." + }, + "B00176": { + "lesson": "K0324", + "objs": [ + "K0324002B", + "K0324003B" + ], + "content": "函数 $y=\\tan x$, $x \\in(-\\dfrac{\\pi}{2}, \\dfrac{\\pi}{2})$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\foreach \\i in {-pi/2,0,pi/2}\n{\\draw [gray!50,dashed] (\\i,-4) -- (\\i,4);};\n\\draw (pi/2,0) node [below] {$\\frac{\\pi}{2}$};\n\\foreach \\i in {-4,-3,-2,-1,0,1,2,3,4}\n{\\draw [gray!50,dashed] (-2,\\i) -- (2,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00177": { + "lesson": "K0324", + "objs": [ + "K0324002B", + "K0324003B" + ], + "content": "函数 $y=\\tan x$ 的大致图像:\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\foreach \\i in {-2*pi,-1.5*pi,-pi,-pi/2,0,pi/2,pi,1.5*pi,2*pi}\n{\\draw [gray!50,dashed] (\\i,-4) -- (\\i,4);};\n\\draw (pi/2,0) node [below] {$\\frac{\\pi}{2}$};\n\\foreach \\i in {-4,-3,-2,-1,0,1,2,3,4}\n{\\draw [gray!50,dashed] (-7,\\i) -- (7,\\i);};\n\\draw (0,1) node [left] {$1$};\n\\draw [->] (-7,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\end{tikzpicture}\n\\end{center}" + }, + "B00178": { + "lesson": "K0324", + "objs": [ + "K0324004B", + "K0324005B", + "K0324006B" + ], + "content": "正切函数的性质:\n\\begin{center}\n\\begin{tabular}{|c|p{20em}|}\\hline 周期性 & \\\\\n\\hline 值域 & \\\\\n\\hline 奇偶性 & \\\\\n\\hline 单调区间 & \\\\\n\\hline\n\\end{tabular}\n\\end{center}" } } \ No newline at end of file