diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index 8e0d37e2..8cc1d1e5 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,146 +1,11 @@ -ans +remark -018366 -(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) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$ +021538 +(20240305)错因: 没写清楚具体角度的三角比的符号的判断过程; 解方程没验根 -018367 -(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) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$ -018369 -(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$ - -009563 -(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) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$ - -018372 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$ - -018373 -$-\dfrac{56}{65}$ - -018375 -$\dfrac{\pi}{3}$ - -009564 -(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$ - -009565 -$-\dfrac{7\sqrt{2}}{26}$ - -018377 -(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$ +021544 +(20240305)错因: 没写清楚具体角度所在范围以及三角比符号的判断过程 018376 -$-\dfrac{4}{5}$ - -018378 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$ - -018379 -证明略 - -018380 -(1) $-1$; (2) $\dfrac{1}{7}$ - -018381 -$-\sqrt{3}$ - -009567 -(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$ - -009568 -$\dfrac{\sqrt{2}}{10}$, $7$ - -009569 -(1) 证明略; (2) 证明略 - -018385 -证明略 - -018386 -$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$ - -018387 -(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$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$ - -024614 -$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$ - -009570 -$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$ - -009571 -$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角 - -009572 -(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$ - -018390 -$\dfrac{\sqrt{6}-\sqrt{2}}{4}$ - -018393 -$\sin 2\alpha=-\dfrac{24}{25}$, $\cos 2\alpha = -\dfrac{7}{25}$, $\tan 2\alpha = \dfrac{24}{7}$ - -018395 -$\cos 3\theta = 4\cos^3\theta-3\cos \theta$ - -018396 -(1) 证明略; (2) 证明略 - -009573 -(1) $\dfrac{1}{4}$; (2) $\dfrac{\sqrt{2}}{2}$; (3) $\dfrac{\sqrt{3}}{6}$ - -018394 -$\sin 4\alpha=\dfrac{336}{625}$; $\cos 4\alpha = -\dfrac{527}{625}$ - -009574 -$\sin 2\alpha=-\dfrac{4}{5}$, $\cos 2\alpha=-\dfrac{3}{5}$, $\tan 2\alpha=\dfrac{4}{3}$ - -009575 -(1) 证明略; (2) 证明略; (3) 证明略 - -018398 -$\dfrac{7}{25}$ - -018401 -$\cos ^2 \dfrac{\alpha}{2}=\dfrac{1+\cos\alpha}{2}$, $\sin ^2 \dfrac{\alpha}{2}=\dfrac{1-\cos\alpha}{2}$, $\tan ^2 \dfrac{\alpha}{2}=\dfrac{1-\cos\alpha}{1+\cos\alpha}$ - -018402 -证明略 - -018403 -证明略 - -018404 -证明略 - -009576 -证明略 - -009577 -证明略 - -009578 -证明略 - -018405 -证明略 - -040387 -$\dfrac{5\pi}{3}$ - -040388 -$-1$ - -040389 -$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$ - -040390 -$-3$ - -040391 -$-2$ - -040392 -$-\dfrac{\sqrt{23}}{4}$ - +(20240305)错因: 没写清楚具体角度所在范围以及三角比符号的判断过程; 解方程没验根 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 59ef5bd7..15c3a3f4 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -506593,7 +506593,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "\\\\\n(20240305)错因: 没写清楚具体角度所在范围以及三角比符号的判断过程; 解方程没验根", "space": "4em", "unrelated": [] }, @@ -596690,7 +596690,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "\\\\\n(20240305)错因: 没写清楚具体角度的三角比的符号的判断过程; 解方程没验根", "space": "4em", "unrelated": [] }, @@ -596870,7 +596870,7 @@ ], "same": [], "related": [], - "remark": "", + "remark": "\\\\\n(20240305)错因: 没写清楚具体角度所在范围以及三角比符号的判断过程", "space": "4em", "unrelated": [] },