diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index b20a32c4..41c7d30c 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -500301,7 +500301,7 @@ }, "018467": { "id": "018467", - "content": "设常数$A>0$, $\\omega>0$, $0<\\varphi<\\pi$, 函数$y=A \\sin (\\omega x+\\varphi)$的部分图像如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [above right] {$O$};\n\\draw [domain = -1:{2*pi/3}, samples = 200] plot (\\x,{2*sin(2*\\x/pi*180+120)});\n\\filldraw ({pi/6},0) circle (0.03) node [below left] {\\small$\\dfrac{\\pi}{6}$};\n\\filldraw ({-pi/12},0) circle (0.03) node [below] {\\small$\\dfrac{\\pi}{12}$};\n\\filldraw (0,2) circle (0.03) node [right] {\\small$2$};\n\\draw [dashed] ({-pi/12},0) --++ (0,2) --(0,2);\n\\end{tikzpicture}\n\\end{center}\n(1) 求$A, \\omega, \\varphi$的值;\\\\\n(2) 求函数$y=A \\sin (\\omega x+\\varphi)$, $x \\in[0, \\dfrac{\\pi}{2}]$的最值.", + "content": "设常数$A>0$, $\\omega>0$, $0<\\varphi<\\pi$, 函数$y=A \\sin (\\omega x+\\varphi)$的部分图像如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [above right] {$O$};\n\\draw [domain = -1:{2*pi/3}, samples = 200] plot (\\x,{2*sin(2*\\x/pi*180+120)});\n\\filldraw ({pi/6},0) circle (0.03) node [below left] {\\small$\\dfrac{\\pi}{6}$};\n\\filldraw ({-pi/12},0) circle (0.03) node [below] {\\small$-\\dfrac{\\pi}{12}$};\n\\filldraw (0,2) circle (0.03) node [right] {\\small$2$};\n\\draw [dashed] ({-pi/12},0) --++ (0,2) --(0,2);\n\\end{tikzpicture}\n\\end{center}\n(1) 求$A, \\omega, \\varphi$的值;\\\\\n(2) 求函数$y=A \\sin (\\omega x+\\varphi)$, $x \\in[0, \\dfrac{\\pi}{2}]$的最值.", "objs": [], "tags": [ "第三单元" @@ -500313,7 +500313,8 @@ "usages": [], "origin": "空中课堂必修第二册三角函数例题与习题", "edit": [ - "20230705\t王伟叶" + "20230705\t王伟叶", + "20240214\t王伟叶" ], "same": [ "030284"