添加关联题24566

题库0.3/Problems.json

@@ -583236,7 +583236,9 @@
         "same": [
             "009552"
         ],
-        "related": [],
+        "related": [
+            "024566"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -666492,6 +666494,31 @@
         "space": "4em",
         "unrelated": []
     },
+    "024566": {
+        "id": "024566",
+        "content": "已知$\\cot \\alpha=\\dfrac{1}{4}$, 求$\\sin \\alpha$、$\\cos \\alpha$及$\\tan \\alpha$.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "4em",
+        "ans": "当$\\alpha$在第一象限时, $\\sin \\alpha =\\frac{4\\sqrt{17}}{17}$, $\\cos \\alpha =\\frac{\\sqrt{17}}{17}$, $\\tan \\alpha=4$;\\\\\n当$\\alpha$在第三象限时, $\\sin \\alpha =-\\frac{4\\sqrt{17}}{17}$,$\\cos \\alpha =-\\frac{\\sqrt{17}}{17}$, $\\tan \\alpha=4$.",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下校本作业-20240214修改",
+        "edit": [
+            "20230209\t王伟叶",
+            "20240214\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "021486"
+        ],
+        "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.",