添加3道关联题

题库0.3/Problems.json

@@ -582631,7 +582631,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023598"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -582662,7 +582664,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023599"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -582817,7 +582821,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023600"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -638005,6 +638011,81 @@
         "space": "4em",
         "unrelated": []
     },
+    "023598": {
+        "id": "023598",
+        "content": "作出函数 $y=1+\\sin x$, $x \\in[-\\pi, \\pi]$ 的大致图像.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-pi,0.1) -- (-pi,0) node [below left] {$-\\pi$};\n\\draw (-0.5*pi,0.1) -- (-0.5*pi,0) node [below] {$-\\frac{\\pi}{2}$};\n\\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (pi,0.1) -- (pi,0) node [below] {$\\pi$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\draw (0.1,-1) -- (0,-1) node [left] {$-1$};\n\\draw [domain = -pi:pi,samples = 100] plot (\\x,{sin(\\x/pi*180)+1});\n\\end{tikzpicture}",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下校本作业-20240116修改",
+        "edit": [
+            "20230209\t王伟叶",
+            "20240116\t朱敏慧"
+        ],
+        "same": [],
+        "related": [
+            "021640"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023599": {
+        "id": "023599",
+        "content": "函数 $y=\\dfrac{1}{1+\\sin x}$ 的定义域为\\blank{100}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "",
+        "ans": "$\\left \\{x|x \\neq-\\dfrac{\\pi}{2}+2k\\pi,k \\in \\mathbf{Z} \\right \\}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下校本作业-20240116修改",
+        "edit": [
+            "20230209\t王伟叶",
+            "20240116\t朱敏慧"
+        ],
+        "same": [],
+        "related": [
+            "021641"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023600": {
+        "id": "023600",
+        "content": "已知$a$为实常数, 作出函数$f(x)=\\sin x$, $x \\in[0, \\dfrac{5}{4} \\pi]$的图像并讨论方程$f(x)=a$的实数解个数.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "当$a \\in (-\\infty, -\\dfrac{\\sqrt{2}}{2})\\cup (1,+\\infty)$ 时，方程实数解个数为$0$个; \\\\\n当$a \\in [-\\dfrac{\\sqrt{2}}{2},0)\\cup \\{1\\}$ 时，方程实数解个数为$1$个; \\\\\n当$a \\in [0,1)$时，方程实数解个数为$2$个",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下校本作业-20240116修改",
+        "edit": [
+            "20230209\t王伟叶",
+            "20240116\t朱敏慧"
+        ],
+        "same": [],
+        "related": [
+            "021646"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",