修改一些题面与答案

题库0.3/Problems.json

@@ -582422,13 +582422,13 @@
     },
     "021458": {
         "id": "021458",
-        "content": "完成下列角度与弧度的换算:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline 角度数 &$15^{\\circ}$&$105^{\\circ}$&$225^{\\circ}$&\\blank{15} &\\blank{15} &\\blank{15} &\\blank{15} \\\\\n\\hline 弧度数 &\\blank{15} &\\blank{15} &\\blank{15} &$\\dfrac{5 \\pi}{3}$&$\\dfrac{9 \\pi}{5}$&$\\dfrac{7 \\pi}{4}$&$\\dfrac{3}{2}$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
+        "content": "完成下列角度与弧度的换算:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline 角度数 &$15^{\\circ}$&$105^{\\circ}$&$225^{\\circ}$& \\underline{\\hbox to 3pt{} (1) \\hbox to 3pt{}} & \\underline{\\hbox to 3pt{} (2) \\hbox to 3pt{}} & \\underline{\\hbox to 3pt{} (3) \\hbox to 3pt{}} & \\underline{\\hbox to 3pt{} (4) \\hbox to 3pt{}} \\\\\n\\hline 弧度数 & \\underline{\\hbox to 3pt{} (5) \\hbox to 3pt{}} & \\underline{\\hbox to 3pt{} (6) \\hbox to 3pt{}} & \\underline{\\hbox to 3pt{} (7) \\hbox to 3pt{}} &$\\dfrac{5 \\pi}{3}$&$\\dfrac{9 \\pi}{5}$&$\\dfrac{7 \\pi}{4}$&$\\dfrac{3}{2}$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
         "objs": [],
         "tags": [
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$\\dfrac{\\pi}{12}$; $\\dfrac{7\\pi}{12}$; $\\dfrac{5\\pi}{4}$; $300^{\\circ}$; $324^{\\circ}$; $315^{\\circ}$; $(\\dfrac{270}{\\pi})^{\\circ}$",
+        "ans": "$300^{\\circ}$; $324^{\\circ}$; $315^{\\circ}$; $(\\dfrac{270}{\\pi})^{\\circ}$; $\\dfrac{\\pi}{12}$; $\\dfrac{7\\pi}{12}$; $\\dfrac{5\\pi}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582441,7 +582441,8 @@
         ],
         "origin": "2025届高一下校本作业",
         "edit": [
-            "20230209\t王伟叶"
+            "20230209\t王伟叶",
+            "20240221\t王伟叶"
         ],
         "same": [],
         "related": [],
@@ -582515,7 +582516,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "(1)$\\frac{\\pi}{3}$;(2)$\\frac{2\\pi}{3}$",
+        "ans": "$\\dfrac{\\pi}{3}$; $\\dfrac{2\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582528,7 +582529,8 @@
         ],
         "origin": "2025届高一下校本作业",
         "edit": [
-            "20230209\t王伟叶"
+            "20230209\t王伟叶",
+            "20240221\t王伟叶"
         ],
         "same": [],
         "related": [],
@@ -582659,13 +582661,13 @@
     },
     "021466": {
         "id": "021466",
-        "content": "用弧度制写出下图中的阴影部分表示的角的集合(包括边界).\\\\\n(1) \\blank{100};\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [gray!25] (0,0) --++ (-45:1.5) arc (-45:90:1.5);\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$} coordinate (x);\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$} coordinate (y);\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (0,0) --++ (-45:1.5) coordinate (T);\n\\draw pic [draw, \"$45^\\circ$\", scale = 0.5, angle eccentricity = 2.5] {angle = T--O--x};\n\\end{tikzpicture}\n\\end{center}\n(2) \\blank{100}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [gray!25] (0,0) --++ (30:1.5) arc (30:150:1.5);\n\\fill [gray!25] (0,0) --++ (-30:1.5) arc (-30:-150:1.5);\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$} coordinate (x);\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$} coordinate (y);\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (0,0) --++ (30:1.5) coordinate (T);\n\\draw (0,0) --++ (-30:1.5) (0,0) --++ (-150:1.5);\n\\draw (0,0) --++ (150:1.5) coordinate (S);\n\\draw pic [draw, \"$30^\\circ$\", scale = 0.5, angle eccentricity = 3] {angle = x--O--T};\n\\draw (-2,0) coordinate (x1);\n\\draw pic [draw, \"$30^\\circ$\", scale = 0.5, angle eccentricity = 3] {angle = S--O--x1};\n\\end{tikzpicture}\n\\end{center}",
+        "content": "用弧度制写出下图中的阴影部分表示的角的集合(包括边界).\\\\\n(1) \\blank{100};\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [pattern = north east lines] (0,0) --++ (-45:1.5) arc (-45:90:1.5);\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$} coordinate (x);\n\\draw [->] (0,-2) coordinate (y')-- (0,2) node [left] {$y$} coordinate (y);\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (0,0) --++ (-45:1.5) coordinate (T);\n\\draw pic [draw, \"$45^\\circ$\", scale = 0.5, angle eccentricity = 2.5] {angle = y'--O--T};\n\\end{tikzpicture}\n\\end{center}\n(2) \\blank{100}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [pattern = north east lines] (0,0) --++ (30:1.5) arc (30:150:1.5);\n\\fill [pattern = north east lines] (0,0) --++ (-30:1.5) arc (-30:-150:1.5);\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$} coordinate (x);\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$} coordinate (y);\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (0,0) --++ (30:1.5) coordinate (T);\n\\draw (0,0) --++ (-30:1.5) (0,0) --++ (-150:1.5);\n\\draw (0,0) --++ (150:1.5) coordinate (S);\n\\draw pic [draw, \"$30^\\circ$\", scale = 0.5, angle eccentricity = 3] {angle = x--O--T};\n\\draw (-2,0) coordinate (x1);\n\\draw pic [draw, \"$30^\\circ$\", scale = 0.5, angle eccentricity = 3] {angle = S--O--x1};\n\\end{tikzpicture}\n\\end{center}",
         "objs": [],
         "tags": [
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "(1) $\\{\\alpha|-\\frac{\\pi}{4}+2k\\pi \\le \\alpha \\le \\frac{\\pi}{2}+2k\\pi,\\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{\\alpha|\\frac{\\pi}{6}+k\\pi \\le \\alpha \\le \\frac{5\\pi}{6}+k\\pi,\\ k \\in \\mathbf{Z}\\}$.",
+        "ans": "(1) $\\{\\alpha|-\\frac{\\pi}{4}+2k\\pi \\le \\alpha \\le \\frac{\\pi}{2}+2k\\pi,\\ k \\in \\mathbf{Z}\\}$; (2) $\\{\\alpha|\\frac{\\pi}{6}+k\\pi \\le \\alpha \\le \\frac{5\\pi}{6}+k\\pi,\\ k \\in \\mathbf{Z}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582679,7 +582681,8 @@
         "origin": "2025届高一下校本作业",
         "edit": [
             "20230209\t王伟叶",
-            "20240131\t王伟叶"
+            "20240131\t王伟叶",
+            "20240221\t王伟叶"
         ],
         "same": [],
         "related": [],