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录入一些答案

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wangweiye7840 2024-02-29 15:56:59 +08:00
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题库0.3/Problems.json
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@ -272844,7 +272844,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\{\\dfrac{\\pi}{2},\\dfrac{11\\pi}{6}\\}$; (2) $\\{x|x=k\\pi+\\dfrac{5\\pi}{24}\\text{或}k\\pi-\\dfrac{11\\pi}{24}, \\ k\\in \\mathbf{Z}\\}$; (3) $\\{x|x=\\dfrac{k\\pi}{3}+\\dfrac{\\pi}{6}, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -272866,7 +272866,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac{\\sqrt{2}}{2}$; (2) $\\dfrac{\\sqrt{3}}{2}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -272888,7 +272888,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$-\\dfrac{7\\sqrt{2}}{26}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -272935,7 +272935,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac{\\sqrt{3}}{2}$; (2) $\\sqrt{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -272957,7 +272957,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\sqrt{2}}{10}$, $7$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -272979,7 +272979,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) 证明略; (2) 证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273001,7 +273001,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\sin C=\\dfrac{220}{221}$, $\\cos C=-\\dfrac{21}{221}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273023,7 +273023,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\sin(\\alpha+\\beta)=\\dfrac{33}{65}$, $\\cos(\\alpha+\\beta)=-\\dfrac{56}{65}$, $\\alpha+\\beta$是第二象限角",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273047,7 +273047,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\sqrt{2}\\sin(\\alpha+\\dfrac{\\pi}{4})$; (2) $2\\sin(\\alpha+\\dfrac{2\\pi}{3})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273137,7 +273137,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273159,7 +273159,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -273181,7 +273181,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504201,7 +504201,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $x=\\dfrac{\\pi}{3}+2k\\pi$或$\\dfrac{2\\pi}{3}+2k\\pi$, $k\\in \\mathbf{Z}$; (2) $x=\\pm \\dfrac{3\\pi}{4}+2k\\pi$, $k\\in \\mathbf{Z}$; (3) $x=k\\pi+\\dfrac{\\pi}{6}$, $k\\in \\mathbf{Z}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504223,7 +504223,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\{\\dfrac{\\pi}{6},\\dfrac{\\pi}{3},\\dfrac{7\\pi}{6},\\dfrac{4\\pi}{3}\\}$; (2) $\\{x|x=2k\\pi+\\dfrac{\\pi}{12}\\text{或}x=2k\\pi-\\dfrac{5\\pi}{12}, \\ k\\in \\mathbf{Z}\\}$; (3) $\\{x|x=\\dfrac{k\\pi}{2}+\\dfrac{\\pi}{4}, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504268,7 +504268,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $x=-\\dfrac{\\pi}{2}+2k\\pi$, $k\\in \\mathbf{Z}$; (2) $x=\\pm \\dfrac{\\pi}{6}+2k\\pi$, $k\\in \\mathbf{Z}$; (3) $x=\\dfrac{\\pi}{4}+k\\pi$, $k\\in \\mathbf{Z}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504338,7 +504338,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\sqrt{6}-\\sqrt{2}}{4}$, $\\dfrac{\\sqrt{6}+\\sqrt{2}}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504360,7 +504360,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$-\\dfrac{56}{65}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504404,7 +504404,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\pi}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504426,7 +504426,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$-\\dfrac{4}{5}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504448,7 +504448,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\dfrac{\\sqrt{3}}{2}$; (2) $\\cos 2\\alpha$; (3) $-\\cos 3x$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504470,7 +504470,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\sqrt{6}-\\sqrt{2}}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504492,7 +504492,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504514,7 +504514,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $-1$; (2) $\\dfrac{1}{7}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504536,7 +504536,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$-\\sqrt{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504624,7 +504624,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504646,7 +504646,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$(-\\dfrac{\\sqrt{2}}{2},\\dfrac{3\\sqrt{2}}{2})$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504668,7 +504668,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "(1) $\\sin(\\alpha+\\dfrac{\\pi}{3})$; (2) $\\sqrt{2}\\sin(\\alpha-\\dfrac{\\pi}{4})$; (3) $5\\sin(\\alpha+\\varphi)$, 其中$\\cos\\varphi=\\dfrac{3}{5}$, $\\sin\\varphi=\\dfrac{4}{5}$; (4) $\\sqrt{a^2+b^2}\\sin(\\alpha+\\varphi)$, 其中$\\cos\\varphi=\\dfrac{a}{\\sqrt{a^2+b^2}}$, $\\sin\\varphi=\\dfrac{b}{\\sqrt{a^2+b^2}}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -504736,7 +504736,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "$\\dfrac{\\sqrt{6}-\\sqrt{2}}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -505002,7 +505002,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -505024,7 +505024,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -505046,7 +505046,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -505068,7 +505068,7 @@
"第三单元" "第三单元"
], ],
"genre": "解答题", "genre": "解答题",
"ans": "", "ans": "证明略",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -677604,7 +677604,7 @@
"第三单元" "第三单元"
], ],
"genre": "4em", "genre": "4em",
"ans": "", "ans": "$\\{\\alpha|\\alpha=2k\\pi\\text{或}\\dfrac{2\\pi}{3}+2k\\pi, \\ k\\in \\mathbf{Z}\\}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744825,7 +744825,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$\\dfrac{5\\pi}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744847,7 +744847,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-1$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744869,7 +744869,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac{\\pi}{3}$或$\\dfrac{4\\pi}{3}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744891,7 +744891,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-3$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744913,7 +744913,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-2$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],
@ -744935,7 +744935,7 @@
"第三单元" "第三单元"
], ],
"genre": "填空题", "genre": "填空题",
"ans": "", "ans": "$-\\dfrac{\\sqrt{23}}{4}$",
"solution": "", "solution": "",
"duration": -1, "duration": -1,
"usages": [], "usages": [],