diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c863d2c6..19fb8b22 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -3991,7 +3991,7 @@ }, "000106": { "id": "000106", - "content": "填空题:\\\\\n(1) 在$\\triangle ABC$中, 若$a^2+b^2+ab=c^2$, 则$C=$\\blank{50};\\\\\n(2) 若$\\sin \\theta =a$, $\\cos \\theta =-2a$, 且$\\theta$为第四象限的角, 则实数$a=$\\blank{50}.\\\\", + "content": "填空题:\\\\\n(1) 在$\\triangle ABC$中, 若$a^2+b^2+ab=c^2$, 则$C=$\\blank{50};\\\\\n(2) 若$\\sin \\theta =a$, $\\cos \\theta =-2a$, 且$\\theta$为第四象限的角, 则实数$a=$\\blank{50}.", "objs": [ "K0315003B", "K0305001B" @@ -4006,7 +4006,8 @@ "usages": [], "origin": "教材复习题", "edit": [ - "20220624\t王伟叶, 余利成" + "20220624\t王伟叶, 余利成", + "20240208\t王伟叶" ], "same": [], "related": [], @@ -4251,7 +4252,7 @@ }, "000115": { "id": "000115", - "content": "(1) 完成下表($\\theta$为弧度数):\n\\begin{center}\n\\begin{tabular}{|c|p{.15\\textwidth}<{\\centering}|p{.15\\textwidth}<{\\centering}|p{.15\\textwidth}<{\\centering}|p{.15\\textwidth}<{\\centering}|p{.15\\textwidth}<{\\centering}|}\n \\hline\n $\\theta$ & $1$ & $0.5$ & $0.1$ & $0.01$ & $0.001$\\\\ \\hline\n $\\sin\\theta$ & & & & &\\\\ \\hline\n $\\dfrac{\\sin\\theta}{\\theta}$ & & & & &\\\\ \\hline\n\\end{tabular}\n\\end{center}\n(2) 观察上表中的数据, 你能发现什么规律?\\\\\n(3) 已知$0<\\theta <\\dfrac \\pi 2$, 利用图形面积公式证明$\\sin \\theta <\\theta <\\tan \\theta$, 并应用该公式说明(2)中猜想的合理性.", + "content": "(1) 完成下表($\\theta$为弧度数):\n\\begin{center}\n\\begin{tabular}{|c|p{.12\\textwidth}<{\\centering}|p{.12\\textwidth}<{\\centering}|p{.12\\textwidth}<{\\centering}|p{.12\\textwidth}<{\\centering}|p{.12\\textwidth}<{\\centering}|}\n \\hline\n $\\theta$ & $1$ & $0.5$ & $0.1$ & $0.01$ & $0.001$\\\\ \\hline\n $\\sin\\theta$ & & & & &\\\\ \\hline\n $\\dfrac{\\sin\\theta}{\\theta}$ & & & & &\\\\ \\hline\n\\end{tabular}\n\\end{center}\n(2) 观察上表中的数据, 你能发现什么规律?\\\\\n(3) 已知$0<\\theta <\\dfrac \\pi 2$, 利用图形面积公式证明$\\sin \\theta <\\theta <\\tan \\theta$, 并应用该公式说明(2)中猜想的合理性.", "objs": [ "K0302002B" ], @@ -4265,7 +4266,8 @@ "usages": [], "origin": "教材复习题", "edit": [ - "20220624\t王伟叶, 余利成" + "20220624\t王伟叶, 余利成", + "20240208\t王伟叶" ], "same": [], "related": [], @@ -4285,7 +4287,7 @@ "J20240513-第一轮复习讲义13解三角形" ], "genre": "解答题", - "ans": "(1) \\textcircled{1} $B$不存在, \\textcircled{2} $B=90^\\circ$, \\textcircled{3} $B=\\arcsin\\dfrac 9{13}$或$\\pi-\\arcsin \\dfrac 9{13}$, \\textcircled{4} $B=30^\\circ$, \\textcircled{5} $B=\\arcsin\\dfrac 9{44}$; (2) 当$0