diff --git a/工具v2/latex编辑题目答案及提示.py b/工具v2/latex编辑题目答案及提示.py index 04d9847b..2d63d6b2 100644 --- a/工具v2/latex编辑题目答案及提示.py +++ b/工具v2/latex编辑题目答案及提示.py @@ -1,5 +1,5 @@ -id_string = "013298,014818,030516,030536,031162" -editor = "徐慧" +id_string = "000001" +editor = "王伟叶" diff --git a/工具v2/logo.ico b/工具v2/logo.ico new file mode 100644 index 00000000..3ceb539f Binary files /dev/null and b/工具v2/logo.ico differ diff --git a/工具v2/关键字筛选题号.py b/工具v2/关键字筛选题号.py index 8f5c4f65..69c1633e 100644 --- a/工具v2/关键字筛选题号.py +++ b/工具v2/关键字筛选题号.py @@ -1,6 +1,6 @@ keywords_dict = { "id":[""], #题号 - "content":["两个"],"content2":["正态"], #题面内容 + "content":["导数"], #题面内容 "objs":[""], #目标代码 "tags":[""], #标签, 如["第二单元"]等 "genre":[""], #题目类型, 填空题, 选择题, 解答题 diff --git a/工具v2/参考答案生成.py b/工具v2/参考答案生成.py index dca63b55..8d1b7f1d 100644 --- a/工具v2/参考答案生成.py +++ b/工具v2/参考答案生成.py @@ -1,5 +1,5 @@ answeringfilepath = r"C:\Users\weiye\Documents\wwy sync\23届" # 要生成答案的路径 -outputfilepath = "临时文件" # 输出文件路径 +outputfilepath = "临时文件/23届" # 输出文件路径 from database_tools import * diff --git a/工具v2/学生讲义制作.py b/工具v2/学生讲义制作.py index aaf08846..d5687fc4 100644 --- a/工具v2/学生讲义制作.py +++ b/工具v2/学生讲义制作.py @@ -1,9 +1,9 @@ -problems = ["1:50"] #题号列表, 每个字符串表示一个分块的题目 notetitle = "测试讲义" #讲义标题, 也是文件标题 +problems = ["1:10","20:25","20001:20005"] #题号列表, 每个字符串表示一个分块的题目 sectiontitles = ["课前","课后","附加"] #小节标题列表, 如果与题号列表长度不符则作为不设小节处理 -consecutivenumbering = False #不同小节是否连续编号, True表示连续编号, False表示每小节从1开始编号 +consecutivenumbering = True #不同小节是否连续编号, True表示连续编号, False表示每小节从1开始编号 answered = True #是否展示答案, True表示展示答案, False表示不展示答案 -spaceflag = True #是否留空格, True表示留空格, False表示不留空格 +spaceflag = False #是否留空格, True表示留空格, False表示不留空格 diff --git a/工具v2/工具面板.py b/工具v2/工具面板.py new file mode 100644 index 00000000..e60e5551 --- /dev/null +++ b/工具v2/工具面板.py @@ -0,0 +1,165 @@ +from tkinter import * +from subprocess import call +import os + +root = Tk() + +root.geometry('500x600') + +root.title('题库0.3工具面板v2') + +def temp(): + pass + +def generate_info(string): + outputstring = "暂无信息" + if string == "寻找空闲题号": + outputstring = '功能: 在题库中列出所有空闲题号.\n1. 按"运行STEP1"按钮后等若干秒, 在终端查看结果.' + elif string == "批量收录题目": + outputstring = '功能: 在一个.tex文件中找到\\item开头的题目并收录到题库.\n'+'0. 选中菜单项后会打开一个编辑窗口, 在编辑窗口中设置\n\t(1) 初始编号;\n\t(2) 题目来源(文件中的%开头的注释行的内容会依次作为此后题目来源的后缀);\n\t(3) .tex文件名(完整路径);\n\t(4) 收录日期及编辑者;\n\t(5) 是否对题目进行编号.\n'+'1. 编辑完成后按"运行STEP1"按钮后等若干秒, 在终端查看结果.' + return outputstring + + +def SetButton(string,openfilelist): + commandname.set(string) + LabelTool.config(text = string) + LabelInfo.config(text = generate_info(string)) + button1.place(x = 10, y = 10) + button1.configure(bg = "green") + for f in openfilelist: + os.system("code -w "+f) + +# 按钮STEP1执行的命令 +def run_command1(): + selectedtool = commandname.get() + call(["python",selectedtool+".py"]) + LabelTool.config(text = selectedtool+"命令执行完毕") + button1.place_forget() + +# 按钮STEP2执行的命令 + +# def run_command2(): +# selectedtool = commandname.get() +# if selectedtool == "添加关联题目": +# call(["python","导入关联题目.py"]) +# elif selectedtool == "修改题目数据库": +# call(["python","修改结果汇入.py"]) +# elif selectedtool == "latex修改题目": +# call(["python","导入latex界面修改的题目内容.py"]) +# LabelTool.config(text = selectedtool+ "STEP2命令执行完毕") +# button2.place_forget() + +commandname = StringVar() +commandname.set("none") +LabelTool = Label(root, text = "请在菜单栏选择工具", height = 1, width = 40, anchor=NW) +LabelTool.place(x=10,y=100) +LabelInfo = Label(root, text = "工具提示信息", height = 20, width = 100, anchor = NW, justify = "left") +LabelInfo.place(x=10,y=140) + +button1 = Button(root, text = "运行", command = run_command1) +# button2 = Button(root, text = "运行STEP2", command = run_command2) +# button3 = Button(root, text = "运行STEP3") + +menubar = Menu(root) + +# 设置 录入 菜单项 +ImportMenu = Menu(menubar, tearoff = False) +menubar.add_cascade(label = "录入", menu = ImportMenu) +ImportMenu.add_command(label = "寻找空闲题号", command = lambda: SetButton("寻找空闲题号",[])) +ImportMenu.add_separator() +ImportMenu.add_command(label = "批量收录题目", command = lambda: SetButton("批量收录题目",["批量收录题目.py"])) +ImportMenu.add_command(label = "添加关联题目", command = lambda: SetButton("添加关联题目",["添加关联题目.py"])) + + + +# 设置 维护 菜单项 +MaintainenceMenu = Menu(menubar, tearoff = False) +menubar.add_cascade(label = "维护", menu = MaintainenceMenu) +MaintainenceMenu.add_command(label = "批量添加字段数据", command = lambda: SetButton("修改metadata",["文本文件/metadata.txt"])) +MaintainenceMenu.add_separator() +MaintainenceMenu.add_command(label = "LaTeX编辑题目答案及提示", command = lambda: SetButton("LaTeX编辑题目答案及提示",["latex编辑题目答案及提示.py"])) +MaintainenceMenu.add_command(label = "json编辑题目综合信息", command = lambda: SetButton("json编辑题目综合信息",["json编辑题目综合信息.py"])) +MaintainenceMenu.add_separator() +MaintainenceMenu.add_command(label = "合并使用记录并排序", command = lambda: SetButton("合并使用记录并排序",[])) +MaintainenceMenu.add_separator() +MaintainenceMenu.add_command(label = "统考数据导入", command = lambda: SetButton("统考数据导入",["统考数据导入.py"])) +MaintainenceMenu.add_command(label = "手动统计结果导入", command = lambda: SetButton("手动统计结果导入",["临时文件/手动统计结果.txt"])) +MaintainenceMenu.add_command(label = "转换手打答案至metadata", command = lambda: SetButton("转换手打答案至metadata",["转换手打答案至metadata.py"])) +MaintainenceMenu.add_separator() +MaintainenceMenu.add_command(label = "移除关联题号", command = lambda: SetButton("移除关联题号",["文本文件/metadata.txt"])) +MaintainenceMenu.add_separator() +MaintainenceMenu.add_command(label = "分类题号字典生成", command = lambda: SetButton("分类题号字典生成",["分类题号字典生成.py"])) + + +# 设置 使用 菜单项 +UseMenu = Menu(menubar, tearoff = False) +menubar.add_cascade(label = "使用", menu = UseMenu) +UseMenu.add_command(label = "关键字筛选题号", command = lambda: SetButton("关键字筛选题号",["关键字筛选题号.py"])) +UseMenu.add_separator() +UseMenu.add_command(label = "学生讲义制作", command = lambda: SetButton("学生讲义制作",["学生讲义制作.py"])) +UseMenu.add_command(label = "教师讲义制作", command = lambda: SetButton("教师讲义制作",["教师讲义制作.py"])) +UseMenu.add_command(label = "批量讲义生成", command = lambda: SetButton("批量讲义生成",["批量讲义生成.py"])) +UseMenu.add_separator() +UseMenu.add_command(label = "文件夹题号清点", command = lambda: SetButton("文件夹题号清点",["文件夹题号清点.py"])) +UseMenu.add_command(label = "参考答案生成", command = lambda: SetButton("参考答案生成",["参考答案生成.py"])) +# UseMenu.add_command(label = "题号选题pdf生成", command = lambda: SetButton("题号选题pdf生成",1,["题号选题pdf生成.py"])) +# UseMenu.add_command(label = "批量题号选题pdf生成", command = lambda: SetButton("批量题号选题pdf生成",1,["批量生成题目pdf.py"])) + + +# 设置 备课组 菜单项 +# BKZMenu = Menu(menubar, tearoff=False) +# menubar.add_cascade(label = "备课组材料相关", menu = BKZMenu) +# BKZMenu.add_command(label = "试卷答案生成", command = lambda: SetButton("试卷答案生成",1,["试卷答案生成.py"])) +# BKZMenu.add_command(label = "题号清单生成", command = lambda: SetButton("题号清单生成",1,["题号清单生成.py"])) +# BKZMenu.add_command(label = "已用题号剔除", command = lambda: SetButton("已用题号剔除",1,["已用题号剔除.py"])) +# BKZMenu.add_command(label = "寻找未赋答案题目", command = lambda: SetButton("寻找未赋答案题目",1,["寻找未赋答案题目.py"])) +# BKZMenu.add_command(label = "错题重做来源清点", command = lambda: SetButton("错题重做来源清点",1,["错题重做来源清点.py"])) +# BKZMenu.add_separator() +# BKZMenu.add_command(label = "备课草稿生成", command = lambda: SetButton("备课草稿生成",1,["备课草稿生成.py"])) +# BKZMenu.add_command(label = "备课讨论稿生成", command = lambda: SetButton("备课讨论稿生成",1,["备课讨论稿生成.py"])) + + +# 设置 目标及标签 菜单项 +ObjTagMenu = Menu(menubar, tearoff = False) +menubar.add_cascade(label = "目标及标签", menu = ObjTagMenu) +ObjTagMenu.add_command(label = "课时名和课时目标制作", command = lambda: SetButton("课时名和课时目标制作",["课时名和课时目标制作.py"])) +# ObjTagMenu.add_command(label = "单元标记转换", command = lambda: SetButton("单元标记转换",1,["单元标记转换.py"])) +# ObjTagMenu.add_separator() +# ObjTagMenu.add_command(label = "目标表体生成", command = lambda: SetButton("目标表体生成",1,["根据范围提取课时目标.py"])) +# ObjTagMenu.add_command(label = "目标pdf生成", command = lambda: SetButton("目标pdf生成",1,["课时目标pdf生成.py"])) +# ObjTagMenu.add_command(label = "课时目标寻找题目", command = lambda: SetButton("课时目标寻找题目",1,["课时目标寻找题目.py"])) +# ObjTagMenu.add_command(label = "课时目标划分信息汇总", command = lambda: SetButton("课时目标划分信息汇总",1,[])) +# ObjTagMenu.add_separator() +# ObjTagMenu.add_command(label = "目标挂钩基础清点", command = lambda: SetButton("目标挂钩清点",1,[])) +# ObjTagMenu.add_command(label = "目标清点及清单生成", command = lambda: SetButton("目标清点及清单生成",1,[])) + +# 设置 相同相似比对 菜单项 +SimRelMenu = Menu(menubar, tearoff= False) +menubar.add_cascade(label = "相同相似", menu = SimRelMenu) +# SimRelMenu.add_command(label = "新题相似相同比对", command = lambda: SetButton("新题相似相同比对",1,["新题相似相同比对.py"])) +# SimRelMenu.add_separator() +# SimRelMenu.add_command(label = "局部相似题目检测", command = lambda: SetButton("局部相似题目检测",1,["局部相似题目检测.py"])) +# SimRelMenu.add_command(label = "相同相似题目标注", command = lambda: SetButton("相同相似题目标注",1,["相同相似题目标注.py"])) +# SimRelMenu.add_separator() +# SimRelMenu.add_command(label = "全局未标注相同题目检测", command = lambda: SetButton("全局未标注相同题目检测",1,[])) + + + +# 设置 其他 菜单项 +OtherMenu = Menu(menubar, tearoff = False) +menubar.add_cascade(label = "其他", menu = OtherMenu) +# OtherMenu.add_command(label = "剪贴板mathpix预处理", command = lambda: SetButton("mathpix预处理",1,[])) +# OtherMenu.add_command(label = "剪贴板带圈数字处理", command = lambda: SetButton("带圈数字处理",1,[])) +# OtherMenu.add_command(label = "剪贴板表格整理", command = lambda: SetButton("剪贴板表格整理",1,[])) +# OtherMenu.add_command(label = "剪贴板单选变多选", command = lambda: SetButton("剪贴板单选变多选",1,[])) + + +menubar.add_command(label = "退出", command = root.destroy) + + + +root.config(menu = menubar) +# root.attributes("-topmost",1) +root.iconbitmap("logo.ico") + +root.mainloop() \ No newline at end of file diff --git a/工具v2/教师讲义制作.py b/工具v2/教师讲义制作.py index 691cea2c..a6f38c47 100644 --- a/工具v2/教师讲义制作.py +++ b/工具v2/教师讲义制作.py @@ -1,9 +1,17 @@ -problems = ["1:500"] #题号列表, 每个字符串表示一个分块的题目 +problems = ["1:5","10:15"] #题号列表, 每个字符串表示一个分块的题目 notetitle = "测试讲义教师版" #讲义标题, 也是文件标题 sectiontitles = ["课前","课后"] #小节标题列表, 如果与题号列表长度不符则作为不设小节处理 -consecutivenumbering = False #不同小节是否连续编号, True表示连续编号, False表示每小节从1开始编号 -topandbottomusagestuple = (2,0) #表示保留得分率最高的使用记录与最低的使用记录的个数, 有负数表示不排列 +consecutivenumbering = True #不同小节是否连续编号, True表示连续编号, False表示每小节从1开始编号 +topandbottomusagestuple = (3,3) #表示保留得分率最高的使用记录与最低的使用记录的个数, 有负数表示不排列 +showobjs = True #是否显示目标, True为显示, False为不显示 +showtags = True #是否显示目标, True为显示, False为不显示 +showans = True #是否显示目标, True为显示, False为不显示 +showsolution = True #是否显示目标, True为显示, False为不显示 +showusages = True #是否显示目标, True为显示, False为不显示 +showorigin = True #是否显示目标, True为显示, False为不显示 +showremark = True #是否显示目标, True为显示, False为不显示 +sectionname = "section" #按何种名称分组, 可选section, subsection, chapter等 from database_tools import * @@ -26,7 +34,7 @@ if sys.platform != "win32": #非win系统用默认字体 -bodystring = GenerateTeacherBodyString(problems,sectiontitles,pro_dict,obj_dict,consecutivenumbering,topandbottomusagestuple) #生成.tex中的内容主体字符串, 用于替换模板中的相应部分 +bodystring = GenerateTeacherBodyString(problems,sectiontitles,pro_dict,obj_dict,sectionname=sectionname, consecutivenumbering=consecutivenumbering, topandbottomusagestuple = topandbottomusagestuple, showobjs = showobjs, showtags = showtags, showans = showans, showsolution = showsolution, showusages = showusages, showorigin = showorigin, showremark = showremark) #生成.tex中的内容主体字符串, 用于替换模板中的相应部分 latex_data = StringSubstitute(r"<<[\s\S]*?待替换[\s\S]*?>>",latex_raw,(notetitle,bodystring)) #替换标题和bodystring SaveTextFile(latex_data,outputfilepath) #保存.tex文件 diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index 94c516e8..74bcb09e 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,758 +1,2277 @@ -usages +ans -022106 -20230620 2025届高一01班 0.881 +021441 +错误, 正确, 错误, 错误 -022107 -20230620 2025届高一01班 0.857 +021442 +D -022108 -20230620 2025届高一01班 0.905 +021443 +C -022109 -20230620 2025届高一01班 0.643 +021444 +A -022110 -20230620 2025届高一01班 0.857 +021445 +C -022111 -20230620 2025届高一01班 0.905 +021446 +D -022112 -20230620 2025届高一01班 0.810 +021447 +$-390^\circ$ -022113 -20230620 2025届高一01班 0.595 +021448 +$304^\circ$, $-56^\circ$ -022114 -20230620 2025届高一01班 0.762 +021449 +$-144^\circ$ -022115 -20230620 2025届高一01班 0.548 +021450 +二, 四 -022116 -20230620 2025届高一01班 0.167 +021451 +(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ -022117 -20230620 2025届高一01班 0.071 +021452 +\begin{tikzpicture}[>=latex] +\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle; +\draw (30:2) -- (0,0) -- (60:2); +\draw [->] (-2,0) -- (2,0) node [below] {$x$}; +\draw [->] (0,-2) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\end{tikzpicture} -022118 -20230620 2025届高一01班 0.810 +021453 +$-1290^{\circ}$;第二象限 -022119 -20230620 2025届高一01班 0.786 +021454 +(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. -022120 -20230620 2025届高一01班 0.619 +021455 +(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. -022121 -20230620 2025届高一01班 0.643 +021456 +C -022122 -20230620 2025届高一01班 0.897 0.841 +021457 +B -022123 -20230620 2025届高一01班 0.964 0.455 +021458 +$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ -022124 -20230620 2025届高一01班 0.655 0.622 +021459 +(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ -022125 -20230620 2025届高一01班 0.970 0.909 0.387 +021460 +$\sqrt{3}$ -022126 -20230620 2025届高一01班 0.929 0.460 0.033 +021461 +(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ -022106 -20230620 2025届高一02班 0.829 +021462 +(1)$16\pi+\frac{2\pi}{3}$,二;\\ +(2)$-18\pi+\frac{4\pi}{3}$,三;\\ +(3)$-2\pi+\frac{7\pi}{5}$,三;\\ +(4)$-2\pi+\frac{3\pi}{4}$,二. -022107 -20230620 2025届高一02班 1.000 +021463 +$\frac{1}{2}$ -022108 -20230620 2025届高一02班 1.000 +021464 +(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. -022109 -20230620 2025届高一02班 0.805 +021465 +(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ +(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ +(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\ +(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. -022110 -20230620 2025届高一02班 0.902 +021466 +(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. -022111 -20230620 2025届高一02班 0.732 +021467 +(1) 第四象限；第四象限；\\ +(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴. -022112 -20230620 2025届高一02班 0.927 +021468 +$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ + +021469 +\begin{tabular}{|c|c|c|c|c|c|} +\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\ +\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\ +\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\ +\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\ +\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\ +\hline +\end{tabular} + +021470 +$2\sqrt{5}$ + +021471 +$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ + +021472 +$ \left( -2,\frac{2}{3} \right)$ + +021473 +$<$ + +021474 +5 + +021475 +2 + +021476 +当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\ +当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\ +当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$. -022113 -20230620 2025届高一02班 0.561 +021477 +当$\alpha$在第二象限时，$ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\ +当$\alpha$在第三象限时，$ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$. -022114 -20230620 2025届高一02班 0.659 +021478 +$-\frac{\sqrt{3}}{4}$ -022115 -20230620 2025届高一02班 0.439 +021479 +(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限. -022116 -20230620 2025届高一02班 0.098 +021480 +$A=\left\{ -2,-0,4 \right\}$ -022117 -20230620 2025届高一02班 0.049 +021481 +(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $[0,3)$ -022118 -20230620 2025届高一02班 0.902 +021482 +\begin{center} +\begin{tabular}{|c|c|c|c|c|c|} +\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\ +\hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\ +\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\ +\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\ +\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\ +\hline +\end{tabular} +\end{center} -022119 -20230620 2025届高一02班 0.732 +021483 +(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ +(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ -022120 -20230620 2025届高一02班 0.585 +021484 +$-\frac{2\sqrt{5}}{5}$;$2$ -022121 -20230620 2025届高一02班 0.683 +021485 +\textcircled{2} \textcircled{4} -022122 -20230620 2025届高一02班 0.959 0.772 +021486 +当$\alpha$在第一象限时，$ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\ +当$\alpha$在第三象限时，$ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$. -022123 -20230620 2025届高一02班 0.996 0.576 +021487 +$\sin k\pi =0$;\\$\cos k\pi=\left\{ + \begin{array}{lc} + $1$, & k=2n \\ + $ -1$ , &k=2n-1\\ + \end{array} +\right.$ ($n \in \mathbf{Z}$). -022124 -20230620 2025届高一02班 0.650 0.439 +021488 +(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\ +(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\ +(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. -022125 -20230620 2025届高一02班 0.976 0.882 0.470 +021489 +第二象限 -022126 -20230620 2025届高一02班 1.000 0.346 0.005 +021490 +(1) 当$\dfrac{\alpha}{2}$在第二象限时，点$P$在第四象限；\\ +当$\dfrac{\alpha}{2}$在第四象限时，点$P$在第二象限.\\ +(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ -022106 -20230620 2025届高一03班 0.921 +021491 +当$m=0$时，$ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\ +当$m=\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\ +当$m=-\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$. -022107 -20230620 2025届高一03班 0.921 +021492 +$-\dfrac{3}{8}$ -022108 -20230620 2025届高一03班 0.921 +021493 +$-\dfrac{1}{20}$ -022109 -20230620 2025届高一03班 0.737 +021494 +$\dfrac{7\sqrt{2}}{4}$ -022110 -20230620 2025届高一03班 0.974 +021495 +$\dfrac{3\sqrt{5}}{5}$ -022111 -20230620 2025届高一03班 0.763 +021496 +$11$ -022112 -20230620 2025届高一03班 0.816 +021497 +$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ -022113 -20230620 2025届高一03班 0.658 +021498 +$\sin ^2 \alpha$ -022114 -20230620 2025届高一03班 0.763 +021499 +$1$ -022115 -20230620 2025届高一03班 0.474 +021502 +$-\dfrac{12}{5}$ -022116 -20230620 2025届高一03班 0.079 +021503 +$-\dfrac{\sqrt{3}}{2}$ -022117 -20230620 2025届高一03班 0.000 +021504 +$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ -022118 -20230620 2025届高一03班 0.895 +021505 +$-\dfrac{\sqrt{11}}{3}$ -022119 -20230620 2025届高一03班 0.789 +021506 +$\dfrac{\pi}{3}$ -022120 -20230620 2025届高一03班 0.632 +021507 +$\left[ 0,\pi \right )$ -022121 -20230620 2025届高一03班 0.632 +021508 +$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ -022122 -20230620 2025届高一03班 0.904 0.838 +021509 +$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ -022123 -20230620 2025届高一03班 0.943 0.530 +021510 +$\cot \alpha$ -022124 -20230620 2025届高一03班 0.776 0.727 +021511 +$-1$ -022125 -20230620 2025届高一03班 0.967 0.868 0.378 +021512 +$-1$ -022126 -20230620 2025届高一03班 0.961 0.395 0.000 +021513 +$ \sin 2-\cos 2$ -022106 -20230620 2025届高一04班 0.902 +021514 +$0$ -022107 -20230620 2025届高一04班 0.951 +021515 +$0$ -022108 -20230620 2025届高一04班 0.902 +021516 +$-\dfrac{\sqrt{1-a^2}}{a}$ -022109 -20230620 2025届高一04班 0.805 +021517 +$-\dfrac{2+\sqrt{3}}{3}$ -022110 -20230620 2025届高一04班 0.927 +021518 +(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. -022111 -20230620 2025届高一04班 0.780 +021519 +(1) $-\dfrac{2}{3}$; \\ +(2) $\dfrac{2}{3}$; \\ +(3) $-\dfrac{\sqrt{5}}{3}$;\\ +(4) $\dfrac{\sqrt{5}}{2}$. -022112 -20230620 2025届高一04班 0.951 +021520 +(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; +(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. -022113 -20230620 2025届高一04班 0.561 +021521 +$\dfrac{2}{5}$ -022114 -20230620 2025届高一04班 0.829 +021522 +$(3,4)$ -022115 -20230620 2025届高一04班 0.463 +021523 +$0$ -022116 -20230620 2025届高一04班 0.073 +021524 +$\sin \alpha$ -022117 -20230620 2025届高一04班 0.024 +021525 +$-\dfrac{1}{5}$ -022118 -20230620 2025届高一04班 0.780 +021526 +(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\ +(2) $-\dfrac{\sqrt{6}}{3}$;\\ +(3) $1$ -022119 -20230620 2025届高一04班 0.805 +021527 +(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$. -022120 -20230620 2025届高一04班 0.634 +021528 +(1) 当$\alpha$在第一象限时, $\sin (2 \pi-\alpha)=-\dfrac{\sqrt{3}}{2}$; +当$\alpha$在第三象限时, $\sin (2 \pi-\alpha)=\dfrac{\sqrt{3}}{2}$.\\ +(2) 当$\alpha$在第一象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=-\sqrt{3}$; +当$\alpha$在第四象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$. -022121 -20230620 2025届高一04班 0.683 +021529 +(1) $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ +(2) $\{x | x=2k \pi \pm \dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ +(3) $\{x | x=k \pi + \dfrac{5\pi}{6},\ k \in \mathbf{Z}\}$;\\ +(4) $\{x | x=2k \pi + \dfrac{5\pi}{6}$ 或$x=2k \pi + \dfrac{3\pi}{2} ,\ k \in \mathbf{Z}\}$;\\ +第二种写法： $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{6}+\dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ +(5) $\{x | x=k \pi - \arctan \dfrac{\sqrt{3}}{2}+ \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ +(6) $\{x | x=\dfrac{2k \pi}{5} + \dfrac{7\pi}{60}$ 或$ x=\dfrac{2k \pi}{5} - \dfrac{13\pi}{60} ,\ k \in \mathbf{Z}\}$;\\ +(7) $\{x | x=k \pi - \dfrac{5\pi}{8}$ 或$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$; -022122 -20230620 2025届高一04班 0.923 0.866 +021530 +(1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12} \}$;\\ +(2) $\{ \dfrac{5\pi}{6} \}$;\\ +(3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12} \}$;\\ +(4) $\{ \dfrac{5\pi}{6} \}$. -022123 -20230620 2025届高一04班 0.976 0.576 +021531 +(1) $\{x | x= \dfrac{2k \pi}{5} ,\ k \in \mathbf{Z}\}$;\\ +(2) $\{x | x= \dfrac{2k \pi}{3} +\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ +(3) $\{x | x= 2k \pi$ 或$x=k \pi +(-1)^k \cdot \dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ +(4) $\{x | x= k \pi+\dfrac{ \pi}{3}$ 或$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$. -022124 -20230620 2025届高一04班 0.728 0.524 +021532 +$\dfrac{3+4\sqrt{3}}{10}$ -022125 -20230620 2025届高一04班 0.927 0.882 0.491 +021533 +$-1$ -022126 -20230620 2025届高一04班 0.976 0.419 0.005 +021534 +$-\dfrac{33}{50}$ -022106 -20230620 2025届高一05班 0.833 +021535 +(1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$; +(2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$; +(3) $0$. -022107 -20230620 2025届高一05班 0.952 +021536 +(1) $\sqrt{3} \sin \alpha$; +(2) $\cos(\alpha-2\beta)$. -022108 -20230620 2025届高一05班 0.905 +021537 +$\dfrac{140}{221}$ -022109 -20230620 2025届高一05班 0.833 +021538 +$\dfrac{2\sqrt{6}-1}{6}$ -022110 -20230620 2025届高一05班 0.952 +021539 +证明略 -022111 -20230620 2025届高一05班 0.857 +021540 +C -022112 -20230620 2025届高一05班 0.952 +021541 +A -022113 -20230620 2025届高一05班 0.690 +021542 +$\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$ -022114 -20230620 2025届高一05班 0.738 +021543 +$\dfrac{8\sqrt{3}-21}{20}$ -022115 -20230620 2025届高一05班 0.667 +021544 +$\dfrac{\pi}{2}$ -022116 -20230620 2025届高一05班 0.167 +021545 +$-\dfrac{2+\sqrt{15}}{6}$ -022117 -20230620 2025届高一05班 0.024 +021546 +$-\dfrac{\sqrt{2}}{2}$ -022118 -20230620 2025届高一05班 0.833 +021547 +$\sin 2\beta$ -022119 -20230620 2025届高一05班 0.786 +021548 +$0$ -022120 -20230620 2025届高一05班 0.619 +021549 +$2-\sqrt{3}$ -022121 -20230620 2025届高一05班 0.738 +021550 +$\dfrac{16}{65}$ -022122 -20230620 2025届高一05班 0.917 0.849 +021551 +$-\dfrac{7}{25}$ -022123 -20230620 2025届高一05班 0.956 0.562 +021552 +$-\dfrac{4\sqrt{14}+3\sqrt{2}}{20}$ -022124 -20230620 2025届高一05班 0.714 0.562 +021553 +$(\dfrac{4\sqrt{3}+3}{2},\dfrac{3\sqrt{3}-4}{2})$ -022125 -20230620 2025届高一05班 0.952 0.952 0.533 +021554 +$-\dfrac{33}{65}$或$\dfrac{63}{65}$ -022126 -20230620 2025届高一05班 0.952 0.409 0.007 +021555 +B -022106 -20230620 2025届高一06班 0.929 +021556 +C -022107 -20230620 2025届高一06班 0.929 +021557 +$-\dfrac{56}{65}$ -022108 -20230620 2025届高一06班 0.833 +021558 +$-3$ -022109 -20230620 2025届高一06班 0.762 +021559 +$\dfrac{3}{4}$ -022110 -20230620 2025届高一06班 0.952 +021560 +$\dfrac{-6+5\sqrt{3}}{3}$ -022111 -20230620 2025届高一06班 0.714 +021561 +$\tan \alpha$ -022112 -20230620 2025届高一06班 0.929 +021562 +$\sqrt{3}$ -022113 -20230620 2025届高一06班 0.738 +021563 +$-\dfrac{\sqrt{3}}{3}$ -022114 -20230620 2025届高一06班 0.667 +021564 +A -022115 -20230620 2025届高一06班 0.405 +021565 +$-\dfrac{17}{31}$ -022116 -20230620 2025届高一06班 0.095 +021566 +$\dfrac{\pi}{4}$ -022117 -20230620 2025届高一06班 0.071 +021567 +(1) $\dfrac{1}{3}$; +(2) $\dfrac{1}{7}$ -022118 -20230620 2025届高一06班 0.810 +021568 +$-\dfrac{1}{5}$ -022119 -20230620 2025届高一06班 0.762 +021569 +当$CD = 1.4$米时，$\tan \angle ACB$最大 -022120 -20230620 2025届高一06班 0.595 +021570 +(1) $2 \sin (\alpha+\dfrac{\pi}{6})$; +(2) $\sqrt{2} \sin (\alpha+\dfrac{7\pi}{4})$. -022121 -20230620 2025届高一06班 0.690 +021571 +$6\cos(\alpha+\dfrac{\pi}{3})$ -022122 -20230620 2025届高一06班 0.937 0.841 +021572 +$2k \pi-\dfrac{\pi}{3}(k\in \mathbf{Z} )$ -022123 -20230620 2025届高一06班 0.952 0.545 +021573 +B -022124 -20230620 2025届高一06班 0.683 0.667 +021574 +$\dfrac{1}{3}$ -022125 -20230620 2025届高一06班 0.976 0.901 0.521 +021575 +$\dfrac{\pi}{12}$或$\dfrac{5\pi}{12}$ -022126 -20230620 2025届高一06班 0.988 0.377 0.007 +021576 +$5$ -022106 -20230620 2025届高一07班 0.952 +021577 +$\dfrac{13}{3}$ -022107 -20230620 2025届高一07班 0.952 +021578 +$-\dfrac{p}{1+q}$ -022108 -20230620 2025届高一07班 0.929 +021579 +$\dfrac{3}{5}$ -022109 -20230620 2025届高一07班 0.667 +021580 +$\dfrac{24}{7}$ -022110 -20230620 2025届高一07班 0.905 +021581 +$-\dfrac{24}{25}$ -022111 -20230620 2025届高一07班 0.810 +021582 +$-\dfrac{15}{17}$ -022112 -20230620 2025届高一07班 0.952 +021583 +$\sin 2 \varphi=\dfrac{4\sqrt{2}}{9}$; +$\cos 2 \varphi=-\dfrac{7}{9}$; +$\tan 2 \varphi=-\dfrac{4\sqrt{2}}{7}$. -022113 -20230620 2025届高一07班 0.595 +021584 +$\dfrac{24}{25}$; $\dfrac{7}{25}$; $\dfrac{24}{7}$ -022114 -20230620 2025届高一07班 0.738 +021585 +(1) $-\dfrac{\sqrt{3}}{3}$;\\ +(2) $\dfrac{3}{4}$. -022115 -20230620 2025届高一07班 0.500 +021586 +$\dfrac{7}{24}$ -022116 -20230620 2025届高一07班 0.119 +021587 +$-\dfrac{2\sqrt{10}}{5}$ -022117 -20230620 2025届高一07班 0.000 +021588 +$1$ -022118 -20230620 2025届高一07班 0.810 +021590 +$1$或$\dfrac{7}{25}$ -022119 -20230620 2025届高一07班 0.762 +021591 +$-\dfrac{\sqrt{2-2a}}{2}$ -022120 -20230620 2025届高一07班 0.595 +021592 +第三象限 -022121 -20230620 2025届高一07班 0.667 +021593 +当$\dfrac{\theta}{2}$在第二象限时， +$\sin \dfrac{\theta}{2}=\dfrac{\sqrt{3}}{3}$, +$\cos \dfrac{\theta}{2}=-\dfrac{\sqrt{6}}{3}$, +$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$;\\ +当$\dfrac{\theta}{2}$在第四象限时， +$\sin \dfrac{\theta}{2}=-\dfrac{\sqrt{3}}{3}$, +$\cos \dfrac{\theta}{2}=\dfrac{\sqrt{6}}{3}$, +$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$. -022122 -20230620 2025届高一07班 0.849 0.873 +021594 +$\dfrac{3}{5}$;$\dfrac{4}{5}$ -022123 -20230620 2025届高一07班 0.976 0.518 +021596 +$\dfrac{2}{3}$ -022124 -20230620 2025届高一07班 0.730 0.479 +021597 +$\cos \alpha-\sin \alpha$ -022125 -20230620 2025届高一07班 0.929 0.873 0.414 +021598 +$\sin \dfrac{ \alpha}{2}$ -022126 -20230620 2025届高一07班 0.952 0.429 0.024 +021599 +(1) $\tan \dfrac{\theta}{2}$; (2) $\sin \alpha$. -022106 -20230620 2025届高一08班 0.821 +021600 +$\dfrac{\sqrt{6}}{2}$ -022107 -20230620 2025届高一08班 0.923 +021601 +$30^{\circ}$或$90^{\circ}$ -022108 -20230620 2025届高一08班 0.846 +021602 +$\sqrt{6}$ -022109 -20230620 2025届高一08班 0.564 +021603 +$55$ -022110 -20230620 2025届高一08班 0.974 +021604 +$\dfrac{\pi}{3}$或$\dfrac{2\pi}{3}$ -022111 -20230620 2025届高一08班 0.821 +021605 +$1: \sqrt{3}: 2$ -022112 -20230620 2025届高一08班 0.897 +021606 +$2$ -022113 -20230620 2025届高一08班 0.718 +021607 +$\dfrac{5}{8}$ -022114 -20230620 2025届高一08班 0.769 +021608 +等腰 -022115 -20230620 2025届高一08班 0.385 +021609 +$\dfrac{3\sqrt{2}}{2}$ -022116 -20230620 2025届高一08班 0.154 +021610 +$\sqrt{3}$ -022117 -20230620 2025届高一08班 0.026 +021611 +$\dfrac{7\pi}{12}$ -022118 -20230620 2025届高一08班 0.795 +021612 +$\dfrac{2\pi}{3}$ -022119 -20230620 2025届高一08班 0.821 +021613 +(1) $\left( 0,9 \right)$; \\ +(2) $\{9\} \cup \left[18,+ \infty \right)$;\\ +(3) $\left( 9,18 \right)$. -022120 -20230620 2025届高一08班 0.538 +021614 +$\dfrac{3\sqrt{7}}{8}$ -022121 -20230620 2025届高一08班 0.718 +021615 +$\sqrt{17}$或$\sqrt{65}$ -022122 -20230620 2025届高一08班 0.966 0.902 +021616 +$\dfrac{\pi}{4}$ -022123 -20230620 2025届高一08班 0.957 0.494 +021617 +\textcircled{1}；\textcircled{2} -022124 -20230620 2025届高一08班 0.679 0.433 +021618 +$a>3$ -022125 -20230620 2025届高一08班 1.000 0.846 0.497 +021619 +$a=\sqrt{21}$和$\sin B=\dfrac{5\sqrt{7}}{14}$ -022126 -20230620 2025届高一08班 0.974 0.423 0.008 +021620 +$\dfrac{2\pi}{3}$ -022106 -20230620 2025届高一09班 0.953 +021621 +$c=\sqrt{6}+\sqrt{2}$;$C=75^\circ$. -022107 -20230620 2025届高一09班 0.953 +021622 +$\dfrac{\sqrt{19}}{2}$ -022108 -20230620 2025届高一09班 0.860 +021623 +周长的最小值为$12$,此时三角形为正三角形；\\ +面积最大值为$4\sqrt{3}$,此时三角形为正三角形. -022109 -20230620 2025届高一09班 0.884 +021624 +$\dfrac{\sqrt{5}}{5}$ -022110 -20230620 2025届高一09班 0.884 +021625 +$\dfrac{2\sqrt{5}}{5}$或$-\dfrac{2\sqrt{5}}{25}$ -022111 -20230620 2025届高一09班 0.814 +021626 +$\dfrac{\sqrt{5}}{5}$或$\dfrac{11\sqrt{5}}{25}$ -022112 -20230620 2025届高一09班 0.907 +021627 +$\left ( 2,2\sqrt{2} \right )$ -022113 -20230620 2025届高一09班 0.721 +021628 +(1) 以$C$为直角的直角三角形；\\ +(2) 以$A$为顶角的等腰三角形；\\ +(3) 以$A$为直角的直角三角形. -022114 -20230620 2025届高一09班 0.837 +021629 +$a=\sqrt{13}$;$R=\dfrac{\sqrt{39}}{3}$. -022115 -20230620 2025届高一09班 0.442 +021630 +$6\sqrt{19}$ -022116 -20230620 2025届高一09班 0.140 +021631 +(1) $x=\arcsin \dfrac{2}{5}$或$\pi-\arcsin \dfrac{2}{5}$;\\ +(2) $x=\pi-\arccos \dfrac{2}{3}$或$\pi+\arccos \dfrac{2}{3}$;\\ +(3) $x=k\pi- \arctan \dfrac{1}{2},k \in \mathbf{Z}$. -022117 -20230620 2025届高一09班 0.000 +021632 +$300\sqrt{3}$ -022118 -20230620 2025届高一09班 0.791 +021633 +证明略 -022119 -20230620 2025届高一09班 0.698 +021634 +$\theta=\dfrac{\pi}{12}$;塔高为$1.5$千米. -022120 -20230620 2025届高一09班 0.535 +021635 +$64.81$米 -022121 -20230620 2025届高一09班 0.744 +021636 +(1) $3.9$千米;(2) $4.0$千米. -022122 -20230620 2025届高一09班 0.907 0.837 +021637 +$2.4$千米 -022123 -20230620 2025届高一09班 0.965 0.515 +021638 +$\dfrac{\pi}{2}$ -022124 -20230620 2025届高一09班 0.705 0.622 +021639 +B -022125 -20230620 2025届高一09班 1.000 0.946 0.427 +021640 -022126 -20230620 2025届高一09班 0.953 0.450 0.019 +(1) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-4,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (-pi,0.1) -- (-pi,0) node [below left] {$-\pi$}; +\draw (-0.5*pi,0.1) -- (-0.5*pi,0) node [below] {$-\frac{\pi}{2}$}; +\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = -pi:pi,samples = 100] plot (\x,{sin(\x/pi*180)+1}); +\end{tikzpicture}\\ +(2) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (0,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (pi/2,0.1) -- (pi/2,0) node [below] {$\frac{\pi}{2}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (1.5*pi,0.1) -- (1.5*pi,0) node [below] {$\frac{3\pi}{2}$}; +\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = 0:2*pi,samples = 100] plot (\x,{-cos(\x/pi*180)}); +\end{tikzpicture} -022106 -20230620 2025届高一10班 0.976 -022107 -20230620 2025届高一10班 1.000 +021641 -022108 -20230620 2025届高一10班 0.976 +(1) 定义域为$\left \{x|x \neq-\dfrac{\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$;\\ +(2) 定义域为$\left \{x|\dfrac{\pi}{2}+2k\pi \leq x \leq \dfrac{3\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$. -022109 -20230620 2025届高一10班 0.929 +021642 -022110 -20230620 2025届高一10班 0.952 +$\left \{x|\dfrac{\pi}{6} \leq x \leq \dfrac{5\pi}{6},k \in \mathbf{Z} \right \}$ -022111 -20230620 2025届高一10班 0.810 -022112 -20230620 2025届高一10班 0.976 +021643 +$2\pi$ -022113 -20230620 2025届高一10班 0.667 +021644 +C -022114 -20230620 2025届高一10班 0.762 +021645 +C -022115 -20230620 2025届高一10班 0.714 +021646 -022116 -20230620 2025届高一10班 0.286 +(1) 当$a \in (-\infty，-\dfrac{\sqrt{2}}{2})\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\ +当$a \in [-\dfrac{\sqrt{2}}{2},0)\cup \{1\}$ 时，方程实数解个数为$1$个；\\ +当$a \in [0,1)$时，方程实数解个数为$2$个.\\ +(2) 当$a \in (-\infty，-1)\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\ +当$a \in (0,1]$时，方程实数解个数为$1$个;\\ +当$a \in \{0,-1\}$时，方程实数解个数为$2$个;\\ +当$a \in (-1,0)$时，方程实数解个数为$3$个. -022117 -20230620 2025届高一10班 0.095 +021647 +(1) $8\pi$; +(2) $\pi$;(3) $\pi$;(4) $2\pi$. -022118 -20230620 2025届高一10班 0.952 +021648 +$3$ -022119 -20230620 2025届高一10班 0.833 +021649 +A -022120 -20230620 2025届高一10班 0.810 +021650 +C -022121 -20230620 2025届高一10班 0.810 +021651 +(1) 假;(1) 假;(3) 真. -022122 -20230620 2025届高一10班 0.929 0.944 +021652 +D -022123 -20230620 2025届高一10班 0.988 0.646 +021653 +(1) $\pi$; (2) $\pi$; (3) $\dfrac{\pi}{2}$; (4) $\dfrac{\pi}{|a|}$. -022124 -20230620 2025届高一10班 0.837 0.810 -022125 -20230620 2025届高一10班 0.982 0.972 0.702 +021654 +$4\sin(\dfrac{\pi x}{2})-2$ -022126 -20230620 2025届高一10班 1.000 0.560 0.005 +021655 +B -022106 -20230620 2025届高一11班 0.930 +021656 +A -022107 -20230620 2025届高一11班 1.000 +021657 -022108 -20230620 2025届高一11班 1.000 +(1) $f(3)=-1$; $f(5)=1$; $f(7)=-1$;\\ +(2) $T=4$. -022109 -20230620 2025届高一11班 0.791 -022110 -20230620 2025届高一11班 0.953 +021658 -022111 -20230620 2025届高一11班 0.860 +$\left [2,4\right] $ -022112 -20230620 2025届高一11班 1.000 +021659 +$\left [-2,2\right] $ -022113 -20230620 2025届高一11班 0.767 +021660 +$ [-\dfrac{3}{2},3] $ -022114 -20230620 2025届高一11班 0.814 +021661 -022115 -20230620 2025届高一11班 0.721 +$ (-\dfrac{\sqrt{3}}{2},1] $ -022116 -20230620 2025届高一11班 0.442 -022117 -20230620 2025届高一11班 0.163 +021662 -022118 -20230620 2025届高一11班 0.907 +$3$; $\left \{x|x=-\dfrac{\pi}{2}+2k\pi,k \in \bf{Z} \right\}$ -022119 -20230620 2025届高一11班 0.860 -022120 -20230620 2025届高一11班 0.698 +021663 +$-3$; $\left \{x|x=-\dfrac{\pi}{12}+k\pi,k \in \bf{Z} \right\}$ -022121 -20230620 2025届高一11班 0.837 +021664 -022122 -20230620 2025届高一11班 1.000 0.926 +当$x=\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \bf{Z}$时，函数的最大值为$\sqrt{13}$;\\ +当$x=-\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \bf{Z}$时，函数的最小值为$-\sqrt{13}$. -022123 -20230620 2025届高一11班 0.981 0.634 +021665 +D -022124 -20230620 2025届高一11班 0.876 0.782 +021666 +C -022125 -20230620 2025届高一11班 0.977 0.946 0.645 +021667 -022126 -20230620 2025届高一11班 0.988 0.698 0.116 +当$\alpha=\dfrac{\pi}{2}-\theta$时，竹竿的影子最长，最长为$\dfrac{\sin(\alpha+\theta)}{\sin \theta}*l$. -022106 -20230620 2025届高一12班 0.955 -022107 -20230620 2025届高一12班 1.000 +021668 +$[-1,1]$ -022108 -20230620 2025届高一12班 0.977 +021669 -022109 -20230620 2025届高一12班 0.886 +$\{x|x\neq 2k\pi,k \in \bf{Z}\}$;$(-\infty,0]$ -022110 -20230620 2025届高一12班 0.864 +021670 +$k=3$或$-3$;$b=-1$ -022111 -20230620 2025届高一12班 0.886 +021671 -022112 -20230620 2025届高一12班 1.000 +当$x=0$时，函数$y$取到最大值，最大值为$0$;\\ +当$x=\dfrac{\pi}{4}$时，函数$y$取到最小值，最小值为$-1$. -022113 -20230620 2025届高一12班 0.773 -022114 -20230620 2025届高一12班 0.773 +021672 -022115 -20230620 2025届高一12班 0.636 +$f(a)=\begin{cases} +a^2+2a+2, & a\leq -1,\\ +1, & -1=latex, scale = 0.7] +\draw [->] (-4,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw ({-pi/12},0.1) -- ({-pi/12},0) node [below left] {$-\frac{\pi}{12}$}; +\draw ({pi/6},0.1) -- ({pi/6},0) node [below] {$\frac{\pi}{6}$}; +\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$}; +\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above] {$\frac{2\pi}{3}$}; +\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = {-pi/12}:{11*pi/12},samples = 100] plot (\x,{sin(2*\x/pi*180+30)}); +\end{tikzpicture}\\ +(2) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1,0) -- (15,0) node [below] {$x$}; +\draw [->] (0,-3) -- (0,3) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (3*pi,0.1) -- (3*pi,0) node [below] {$\frac{3\pi}{2}$}; +\draw (4*pi,0.1) -- (4*pi,0) node [below] {$4\pi$}; +\draw (0.1,2) -- (0,2) node [left] {$2$}; +\draw (0.1,-2) -- (0,-2) node [left] {$-2$}; +\draw [domain =0:4*pi,samples = 100] plot (\x,{2*sin(0.5*\x/pi*180)}); +\end{tikzpicture}\\ +(3) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1) -- (0,1) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (0.25*pi,0.1) -- (0.25*pi,0) node [below] {$\frac{\pi}{4}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$}; +\draw (0.75*pi,0.1) -- (0.75*pi,0) node [above] {$\frac{3\pi}{4}$}; +\draw (0.1,0.5) -- (0,0.5) node [left] {$\frac{1}{2}$}; +\draw (0.1,-0.5) -- (0,-0.5) node [left] {$-\frac{1}{2}$}; +\draw [domain =0:pi,samples = 100] plot (\x,{0.5*sin(2*\x/pi*180)}); +\end{tikzpicture}\\ +(4) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1.5,0) -- (3.5,0) node [below] {$x$}; +\draw [->] (0,-5.5) -- (0,5.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw ({-pi/3},0.1) -- ({-pi/3},0) node [below left] {$-\frac{\pi}{3}$}; +\draw ({-pi/12},0.1) -- ({-pi/12},0) node [above left] {$-\frac{\pi}{12}$}; +\draw ({pi/6},0.1) -- ({pi/6},0) node [below right] {$\frac{\pi}{6}$}; +\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$}; +\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above right] {$\frac{2\pi}{3}$}; +\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$}; +\draw (0.1,5) -- (0,5) node [left] {$5$}; +\draw (0.1,-5) -- (0,-5) node [below left] {$-5$}; +\draw [domain = {-4*pi/12}:{2*pi/3},samples = 100] plot (\x,{5*sin(2*\x/pi*180-60)}); +\end{tikzpicture} + + +021695 +$4\pi$;$4$. + +021696 +$f(x)=4\sin(x+\dfrac{\pi}{6})$ + +021697 + +(1) $f(x)=\dfrac{\sqrt{3}}{2}\sin(3x+\pi)+\dfrac{\sqrt{3}}{2};$\\ +(2) $[-\dfrac{\pi}{2}+\dfrac{2k\pi}{3},-\dfrac{\pi}{6}+\dfrac{2k\pi}{3}],k \in \bf{Z}$;\\ +(3) 函数最大值为$\sqrt{3}$,此时$x$值为${x|x=-\dfrac{\pi}{6}+\dfrac{2k\pi}{3},k \in \bf{Z}}$ + +021698 +$x=\pi+2k\pi,k \in \bf{Z}$ + +021699 +纵;伸长; $3$ + +021700 +缩短; $\dfrac{1}{2}$; 缩短; $\dfrac{1}{3}$. + +021701 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{3})$ + +021702 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{6})$ + +021703 +$f(x)=2\sin(\dfrac{1}{3}x+\dfrac{\pi}{6})$ + +021704 +$x=\dfrac{\pi}{3}+2k\pi,k \in \bf{Z}$; $(-\dfrac{2\pi}{3}+2k\pi,0),k \in \bf{Z}$. + +021705 +C + +021706 +左; $\dfrac{\pi}{8}$. + +021707 +$f(x)=\sin(2x+\dfrac{\pi}{2})$, +$g(x)=\sin x$. + +021708 +(1) $\sqrt{2}$; +(2) $g(x)=2\cos(\dfrac{1}{2}x-\dfrac{\pi}{3}) $, 单调递减区间为$[\dfrac{2\pi}{3}+4k\pi,\dfrac{8\pi}{3}+4k\pi],k \in \bf{Z}$. + +021709 +(1) $2\pi$; (2) $1$; (3) $\dfrac{\pi}{2}$. + +021710 +(1) $[0,\dfrac{\pi}{2})$, $(\dfrac{3\pi}{2},2\pi]$; \\ +(2) $[0,\dfrac{\pi}{2})$, $(\dfrac{\pi}{2},\pi]$. + +021711 +(1) 奇函数; (2) 偶函数. + +021712 +$[-5,+\infty)$ + +021713 +(1) $<$; (2) $>$; (3) $>$; (4)$<$. + +021714 + \textcircled{3} + +021715 + +最小值为$-\dfrac{\sqrt{3}}{3}$，此时$x=-\dfrac{\pi}{3}$. + + +021716 + +(1) $ \{x|x \neq \dfrac{k\pi}{2},k \in \bf{Z}\} $;\\ +(2) 单调增区间为$(-\dfrac{\pi}{2}+\dfrac{k\pi}{2},\dfrac{k\pi}{2}), k \in \bf{Z}$. + +021717 +$\{x|x\neq \dfrac{\pi}{4}-\dfrac{1}{2}+\dfrac{k\pi}{2},k \in \bf{Z} \}$ + +021718 +$(-\dfrac{\pi}{4}+\dfrac{k\pi}{3},\dfrac{\pi}{12}+\dfrac{k\pi}{3}), k \in \bf{Z}$ + +021719 +B + +021720 + +定义域为$ \{x|x \neq \dfrac{7\pi}{5}+2k\pi,k \in \bf{Z}\} $;\\ +严格增区间为$(-\dfrac{3\pi}{5}+2k\pi,\dfrac{7\pi}{5}+2k\pi), k \in \bf{Z}$. + +021721 +函数零点为$x=\dfrac{2k\pi}{5}+2k\pi,k \in \bf{Z}$. + +021722 +(1) 假命题; (2) 假命题; (3) 假命题; (4) 真命题. + +021723 + $[-4,2+4\sqrt{3}]$ + +021724 + +最大张角的正切值为$\dfrac{\sqrt{2}}{4}$, 此时学生距离时钟$\sqrt{0.18}$米. + +021726 +A + +021727 +C + +021728 +B + +021729 +单位圆 + +021730 +B + +021731 +$\overrightarrow{CD}$ + +021732 +$\overrightarrow{AC}$ + +021733 + +(1) 假命题; (2) 真命题; (3) 假命题; (4) 假命题. + + +021734 + +(1) $\overrightarrow{DB}$; $\overrightarrow{FE}$.\\ +(2) $\overrightarrow{ED}$; $\overrightarrow{CF}$; $\overrightarrow{FA}$.\\ +(3) $\overrightarrow{EF}$; $\overrightarrow{AD}$; $\overrightarrow{DA}$; $\overrightarrow{DB}$; $\overrightarrow{BD}$; $\overrightarrow{AB}$; $\overrightarrow{BA}$. + +021735 +$40$ + +021736 +$40$ + +021737 +$2$ + +021739 +$-3\overrightarrow {a}+6 \overrightarrow {b}$ + +021740 +$7 \overrightarrow {a}-2 \overrightarrow {b}- \overrightarrow {c}$ + +021741 +(1) 假命题; (2) 真命题; (3) 假命题; (4) 真命题. + +021742 + +(1) $\overrightarrow {AB}=\dfrac{1}{2}\overrightarrow {a}-\dfrac{1}{2}\overrightarrow {b}$;\\ +(2) $\overrightarrow {BC}=\dfrac{1}{2}\overrightarrow {a}+\dfrac{1}{2}\overrightarrow {b}$. + +021743 +$\lambda=\dfrac{1}{3}$ + +021744 +$x=2$; $y=1$. + +021745 +(2) $m=1$或$-1$. + +021746 +$\overrightarrow{DC}=\dfrac{1}{2}\overrightarrow{a}$;\\ $\overrightarrow{DC}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$;\\ +$\overrightarrow{MN}=-\dfrac{1}{4}\overrightarrow{a}-\overrightarrow{b}$. + + +021747 +$\overrightarrow{0}$ + +021748 +$\dfrac{2}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$ + +021749 +A + +021750 +B + +021751 +C + +021752 +$\sqrt{3}$ + +021753 +$-\dfrac{3\sqrt{3}}{2}$ + +021754 +等边三角形 + +021755 +$\dfrac{\pi}{4}$ + +021756 +$\dfrac{2\pi}{3}$ + +021757 +$-10\sqrt{2}$ + +021758 +$\dfrac{4}{3}$ + +021759 +$-\dfrac{2}{3}\overrightarrow {a}$ + +021760 +B + +021761 +B + +021762 +A + +021763 +$7$ + +021764 +$2$ + +021765 +C + +021766 +外心; 重心; 垂心. + +021767 +$\dfrac{\pi}{3}$ + +021768 +$-25$ + +021769 +$\lambda=\dfrac{7}{12}$ + +021770 +$AB=8$ + +021771 +$t=\dfrac{1}{3}$ + +021772 + +(1) $(\overrightarrow {a}-\overrightarrow {b}) \cdot \overrightarrow {c}=\overrightarrow {a} \cdot \overrightarrow {c}- \overrightarrow {b} \cdot \overrightarrow {c}=1*1*(-\dfrac{1}{2})-1*1*(-\dfrac{1}{2})=0;\\$ +(2) $k<0$或$k>2$. + +021773 +$[2,5]$ + +021774 +$\arccos \dfrac{4}{5}$ + +021775 +$\overrightarrow{OP}=\dfrac{3}{11}\overrightarrow {a}+\dfrac{2}{11}\overrightarrow {b}$ + +040018 +(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$ + +040019 +(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$ + +040020 +(1) $2k\pi+\dfrac{\pi}{2}$; (2) $2k\pi+\dfrac{3\pi}{2}$; (3) $2k\pi+\dfrac{7\pi}{6}$; (4) $k\pi+\dfrac{\pi}{4}$; (5) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$ + +040021 +(1) $k \times 360^{\circ}+60^{\circ}$;\\ +(2) $k \times 360^{\circ}+330^{\circ}$; \\ +(3) $k \times 360^{\circ}-210^{\circ}$; \\ +(4) $k \times 180^{\circ}-45^{\circ}$; \\ +(5) $k \times 90^{\circ}+50^{\circ}$ + +040022 +(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$ + +040023 +(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$ + +040024 +$18$ + +040025 +$3$,$-2$ + +040026 +(1) $1037$; (2) $-4k+53$; (3) $500$ + +040027 +$-2n+10$ + +040028 +15 + +040029 +$7$ + +040030 +$(4,\dfrac{14}{3}]$ + +040031 +$2n-1$ + +040032 +$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$ + +040033 +$200$ + +040034 +略 + +040035 +$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$) + +040036 +$6n-3$ + +040057 +$\dfrac{19}{28}\sqrt{7}$ + +040058 +$\dfrac{79}{156}$ + +040059 +$2$ + +040060 +$-\dfrac{\sqrt{1-m^2}}{m}$ + +040061 +$-\dfrac{1}{5}, \dfrac{1}{5}$ + +040062 +$-\dfrac{1}{3}, 3$ + +040063 +$\dfrac{1}{2}, -2$ + +040064 +$\dfrac{\sqrt{6}}{3}$ + +040065 +$\dfrac{1}{3}, -\dfrac{9}{4}$ + +040066 +$\dfrac{1}{3}, \dfrac{7}{9}$ + +040067 +$\pm\dfrac{\sqrt{2}}{3}$ + +040068 +$\dfrac{1}{4}, \dfrac{2}{5}$ + +040069 +$\dfrac{1-\sqrt{17}}{4}$ + +040070 +(1) 三； (2) 三 + +040071 +(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$ + +040072 +(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$ + +040073 +略 + +040074 +$-\dfrac{10}{9}$ + +040075 +$a_n=\dfrac{1}{3n-2}$ + +040076 +$a_n=\dfrac{1}{n}$ + +040077 +$(n-\dfrac{4}{5})5^n$ + +040078 +$2^{n+1}-3$ + +040079 +$1078$ + +040080 +$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$ + +040081 +(1) 略； (2) $n^2$ + +040082 +(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$ + +040083 +$\dfrac{\sqrt{3}}{2}$ + +040084 +$0$ + +040085 +$\{0,-2\pi\}$ + +040086 +$-\dfrac{\pi}6,\dfrac 56\pi$ + +040087 +$\cot \alpha$ + +040088 +$7+4\sqrt{3}$ + +040089 +$\dfrac{\sqrt{2}-\sqrt{6}}{4}$ + +040090 +$\dfrac{\sqrt{3}+\sqrt{35}}{12}$ + +040091 +$\dfrac 12$ + +040092 +$5$ + +040093 +$-\dfrac 12$ + +040094 +$\dfrac{\pi}{12}$ + +040095 +$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$ + +040096 +$\dfrac 43 \pi$ + +040097 +\textcircled{4} + +040098 +C + +040099 +$\dfrac{-2\sqrt{2}-\sqrt{3}}6$ + +040100 +$-\dfrac 7{25}$ + +040101 +$-\dfrac {\pi}3$ + +040102 +$(-\dfrac {12}{13}, \dfrac{5}{13})$ + +040103 +$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$ + +040104 +略 + +040105 +$\dfrac {171} {221}, -\dfrac {21} {221}$ + +040106 +$\{-\pi\}$ + +040107 +$\dfrac{8\sqrt{2}-3}{15}$ + +040108 +$\sin \theta$ + +040109 +$-\dfrac{56}{65}$ + +040110 +$\dfrac {\pi}4$ + +040111 +略 + +040112 +略 + +040181 +$\dfrac 7{25}$ + +040182 +$-\dfrac{\pi}3+2k\pi,k \in \mathbf{Z}$ + +040183 +$\dfrac{4\sqrt{3}-3}{10}$ + +040184 +$\dfrac 17$ + +040185 +$4\sqrt{2} \sin(\alpha+\dfrac {7}{4}\pi))$ + +040186 +$3$ + +040187 +$\dfrac 32$ + +040188 +$\sqrt{3}$ + +040189 +$2$ + +040190 +$\dfrac {13}{18}$ + +040191 +$\dfrac{7}{4}\pi$ + +040192 +$\dfrac{64}{25}$ + +040193 +C + +040194 +A + +040195 +B + +040196 +C + +040197 +$-\dfrac{\pi}6$ + +040198 +$\dfrac 23 \pi$ + +040199 +$\dfrac 32$ + +040200 +$\sqrt{1-k}$ + +040201 +$-\dfrac{484}{729}$ + +040131 +$-\dfrac{25}{12}$ + +040132 +$\dfrac 52$ + +040133 +$-\dfrac{\pi}4$ + +040134 +$-\dfrac 12$ + +040135 +$\dfrac 6{19}$ + +040136 +$-\dfrac {\sqrt{3}}3$ + +040137 +$\dfrac 3{22}$ + +040138 +$4$ + +040139 +$-\dfrac{63}{65}$ + +040226 +$\dfrac 49 \sqrt{2}$ + +040227 +$\sin \theta \cos \theta$ + +040228 +$-\dfrac1{16}$ + +040229 +$\dfrac 32$ + +040230 +$\dfrac{13}{18}$ + +040231 +$-2-\sqrt{7}$ + +040232 +$\sin{\dfrac{\alpha}2}$ + +040233 +$0$ + +040234 +$\dfrac{120}{169}$ + +040235 +$3$或$5$ + +040236 +$\pi-\arcsin{\dfrac{24}{25}}$ + +040237 +$\arcsin{\dfrac{3\sqrt{10}}{10}}$或$\arcsin{\dfrac{\sqrt{10}}{10}}$ + +040238 +$60^{\circ}$或$120^{\circ}$ + +040239 +$\dfrac 23 \pi$ + +040240 +$8$ + +040241 +\textcircled{4} + +040242 +$\dfrac 35$或$\dfrac{24}{25}$或$\dfrac{3\sqrt{10}}{10}$或$\dfrac{\sqrt{10}}{10}$ + +040243 +(1)$\angle A=75^{\circ}, \angle B=45^{\circ}, a=\sqrt{2}+\sqrt{6}$\\ +(2) $\angle B=60^{\circ}, \angle C=75^{\circ}, c=\sqrt{6}+3\sqrt{2}$或 +$\angle B=120^{\circ}, \angle C=15^{\circ}, c=3\sqrt{2} - \sqrt{6}$ + +040244 +$\dfrac 12$ + +040245 +$\dfrac 12 \pm \dfrac{\sqrt{6}}5$ + +040246 +$-\dfrac7{25}$ + +040247 +$\dfrac {\sqrt{2}} 2 +\dfrac 14$ + +040248 +$90^\circ$ + +040249 +$\dfrac 1{a}$ + +040250 +$-\dfrac{16}{65}$ + +040251 +$\dfrac{24}{13}$ + +040252 +$\dfrac{\sqrt{11}}{6}$ + +040253 +直角三角形 + +040254 +$120^\circ$ + +040255 +$-\dfrac{48}{49}$ + +040256 +等边三角形 + +040257 +等腰三角形 + +040258 +等腰或直角三角形 + +040259 +$30^\circ$ + +040260 +$30^\circ$或$90^\circ$或$150^\circ$ + +040261 +$2\sqrt{7}$ + +040262 +$\dfrac 12$ + +040263 +$(0,\dfrac{\pi}4]$ + +040264 +(1) $\dfrac 23 \pi$; (2) 等腰钝角三角形 + +040265 +(1) $\dfrac{\sqrt{3}}6$; (2) $\dfrac{\sqrt{39}+\sqrt{3}}2$ + +040266 +$\{x|\dfrac{\pi}6+2k\pi \le x \le \dfrac 56 \pi+2k\pi, k \in \mathbb{Z} \}$ + +040267 +$[0,3)$ + +040268 +$4$ + +040269 +$\pi$ + +040270 +$\pi$ + +040271 +$\dfrac{\pi}{2}$ + +040272 +$-\sin{\dfrac 12 -1}$ + +040273 +\textcircled{2}\textcircled{3}\textcircled{5} + +040274 +等腰直角三角形 + +040275 +$\{x|\dfrac{\pi}4+2k\pi \le x \le \dfrac 45 \pi+2k\pi, k \in \mathbb{Z} \}$ + +040276 +$4\pi$ + +040277 +$\dfrac{\pi}{2}$ + +040278 +$\sqrt{5}$ + +040279 +$12$ + +040280 +$6+\sqrt{15}$ + +040281 +\textcircled{3} \textcircled{4} + +040282 +$(1)b=1,c=\sqrt{13}$;\\ +$(2)$等腰三角形或直角三角形 + +040396 +$\{x|2k\pi+\dfrac{\pi}4