91 lines
3.7 KiB
Plaintext
91 lines
3.7 KiB
Plaintext
ans
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018434
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\begin{tikzpicture}[>=latex]
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\draw [->] (-1,0) -- (7,0) node [below] {$x$};
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\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\draw [domain = 0:{2*pi}, samples = 100] plot (\x,{1-sin(\x*180/pi)});
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\draw (0,1) node [left] {$1$} (0,2) node [left] {$2$};
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\draw [dashed] ({pi/2*3},2) -- (0,2);
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\draw ({pi/2},0) node [below] {$\frac{\pi}{2}$} ({pi*3/2},0) node [below] {$\frac{3\pi}{2}$};
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\draw (pi,0) node [below] {$\pi$} (2*pi,0) node [below] {$2\pi$};
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\draw [dashed] (2*pi,0) --++ (0,1) -- (0,1) (pi,0) --++ (0,1) (3*pi/2,0) --++ (0,2);
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\end{tikzpicture}
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取值范围为$(0,\pi)$
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018435
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\begin{tikzpicture}[>=latex]
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\draw [->] (-2,0) -- (5.5,0) node [below] {$x$};
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\draw [->] (0,-0.5) -- (0,3.5) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\draw [domain = -pi/2:{3*pi/2}, samples = 100] plot (\x,{2-sin(\x*180/pi)});
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\draw [dashed] (-pi/2,0) --++ (0,3) --++ (2*pi,0) --++ (0,-3) (0,2) --++ (pi,0) --++ (0,-2) (0,1) --++ (pi/2,0) --++ (0,-1);
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\draw (-pi/2,0) node [below] {$\frac{\pi}{2}$} (pi/2,0) node [below] {$\frac{\pi}{2}$} (pi,0) node [below] {$\pi$} (3*pi/2,0) node [below] {$\frac{3\pi}{2}$};
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\draw (0,1) node [left] {$1$} (0,2) node [above right] {$2$} (0,3) node [above right] {$3$};
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\end{tikzpicture}
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018436
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$\dfrac{1}{2}$或$-\dfrac{3}{2}$
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009592
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\begin{tikzpicture}[>=latex]
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\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};
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\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw [domain = -pi:pi, samples = 100] plot (\x,{sin(\x*180/pi)});
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\draw [dashed] (-pi/2,0) --++ (0,-1) -- (0,-1) (pi/2,0) --++ (0,1) -- (0,1);
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\draw (-pi/2,0) node [above] {$-\frac{\pi}{2}$} (pi/2,0) node [below] {$\frac{\pi}{2}$};
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\draw (0,1) node [left] {$1$} (0,-1) node [right] {$-1$};
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\end{tikzpicture}
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009593
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\begin{tikzpicture}[>=latex]
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\draw [->] (-0.5,0) -- (7,0) node [below] {$x$};
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\draw [->] (0,-1) -- (0,2) node [left] {$y$};
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\draw (0,0) node [below right] {$O$};
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\draw [domain = 0:2*pi, samples = 100] plot (\x,{1/2-sin(\x*180/pi)});
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\draw [dashed] (2*pi,0.5) -- (0,0.5) (pi/2,0) --++ (0,-0.5) -- (0,-0.5) (3*pi/2,0) --++ (0,1.5) -- (0,1.5);
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\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (pi/2,0) node [above] {$\frac{\pi}{2}$};
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\draw (0,0.5) node [left] {$\frac{1}{2}$} (0,1.5) node [left] {$\frac{3}{2}$} (0,-0.5) node [left] {$-\frac{1}{2}$};
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\end{tikzpicture}
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$y>0$时$x$的取值范围为$[0,\dfrac{\pi}{6})\cup (\dfrac{5\pi}{6},2\pi]$; $y<0$时$x$的取值范围为$(\dfrac{\pi}{6},\dfrac{5\pi}{6})$
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009594
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\begin{tikzpicture}[>=latex,scale = 0.5]
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\draw [->] (-7,0) -- (7,0) node [below] {$x$};
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\draw [->] (0,-1.5) -- (0,3.5) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\draw [dashed, domain = -7:7, samples = 100] plot (\x,{sin(\x/pi*180)});
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\draw [domain = -7:7, samples = 100] plot (\x,{2+sin(\x/pi*180)});
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\end{tikzpicture}
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$y=2+\sin x$的图像由$y=\sin x$的图像向上平移$2$单位得到
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018437
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$(-\dfrac{2\pi}{3},-\dfrac{\pi}{3})\cup (\dfrac{\pi}{3},\dfrac{2\pi}{3})$
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018438
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$(1,3)$
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023601
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\begin{tikzpicture}[>=latex, scale = 0.6]
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\draw [->] (-7,0) -- (7,0) node [below] {$x$};
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\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\draw [domain = 0:2*pi,samples = 200] plot (\x,{sin(\x/pi*180)}) plot (-\x,{sin(\x/pi*180)});
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\draw [dashed] (pi/2,0) --++ (0,1) -- (-pi/2,1) --++ (0,-1) (3*pi/2,0) --++ (0,-1) -- (-3*pi/2,-1) --++ (0,1);
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\draw (0,1) node [below left] {$1$} (0,-1) node [below left] {$-1$};
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\draw (pi/2,0) node [below] {$\frac{\pi}{2}$} (-pi/2,0) node [below] {$-\frac{\pi}{2}$};
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\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (-3*pi/2,0) node [below] {$-\frac{3\pi}{2}$};
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\end{tikzpicture}
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024726
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$\dfrac{16}{65}$或$\dfrac{56}{65}$
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040264
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(1) $\dfrac 23 \pi$; (2) 顶角为$120^\circ$的等腰三角形
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024727
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$\dfrac{\sqrt{5}-1}{4}$
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