ans

018434
\begin{tikzpicture}[>=latex]
\draw [->] (-1,0) -- (7,0) node [below] {$x$};
\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\draw [domain = 0:{2*pi}, samples = 100] plot (\x,{1-sin(\x*180/pi)});
\draw (0,1) node [left] {$1$} (0,2) node [left] {$2$};
\draw [dashed] ({pi/2*3},2) -- (0,2);
\draw ({pi/2},0) node [below] {$\frac{\pi}{2}$} ({pi*3/2},0) node [below] {$\frac{3\pi}{2}$};
\draw (pi,0) node [below] {$\pi$} (2*pi,0) node [below] {$2\pi$};
\draw [dashed] (2*pi,0) --++ (0,1) -- (0,1) (pi,0) --++ (0,1) (3*pi/2,0) --++ (0,2);
\end{tikzpicture}
取值范围为$(0,\pi)$

018435
\begin{tikzpicture}[>=latex]
\draw [->] (-2,0) -- (5.5,0) node [below] {$x$};
\draw [->] (0,-0.5) -- (0,3.5) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\draw [domain = -pi/2:{3*pi/2}, samples = 100] plot (\x,{2-sin(\x*180/pi)});
\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);
\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] {$\frac{3\pi}{2}$};
\draw (0,1) node [left] {$1$} (0,2) node [above right] {$2$} (0,3) node [above right] {$3$};
\end{tikzpicture}

018436
$\dfrac{1}{2}$或$-\dfrac{3}{2}$

009592
\begin{tikzpicture}[>=latex]
\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};
\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};
\draw (0,0) node [below right] {$O$};
\draw [domain = -pi:pi, samples = 100] plot (\x,{sin(\x*180/pi)});
\draw [dashed] (-pi/2,0) --++ (0,-1) -- (0,-1) (pi/2,0) --++ (0,1) -- (0,1);
\draw (-pi/2,0) node [above] {$-\frac{\pi}{2}$} (pi/2,0) node [below] {$\frac{\pi}{2}$};
\draw (0,1) node [left] {$1$} (0,-1) node [right] {$-1$};
\end{tikzpicture}

009593
\begin{tikzpicture}[>=latex]
\draw [->] (-0.5,0) -- (7,0) node [below] {$x$};
\draw [->] (0,-1) -- (0,2) node [left] {$y$};
\draw (0,0) node [below right] {$O$};
\draw [domain = 0:2*pi, samples = 100] plot (\x,{1/2-sin(\x*180/pi)});
\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);
\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (pi/2,0) node [above] {$\frac{\pi}{2}$};
\draw (0,0.5) node [left] {$\frac{1}{2}$} (0,1.5) node [left] {$\frac{3}{2}$} (0,-0.5) node [left] {$-\frac{1}{2}$};
\end{tikzpicture}
$y>0$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$(\dfrac{\pi}{6},\dfrac{5\pi}{6})$

009594
\begin{tikzpicture}[>=latex,scale = 0.5]
\draw [->] (-7,0) -- (7,0) node [below] {$x$};
\draw [->] (0,-1.5) -- (0,3.5) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\draw [dashed, domain = -7:7, samples = 100] plot (\x,{sin(\x/pi*180)});
\draw [domain = -7:7, samples = 100] plot (\x,{2+sin(\x/pi*180)});
\end{tikzpicture}
$y=2+\sin x$的图像由$y=\sin x$的图像向上平移$2$单位得到

018437
$(-\dfrac{2\pi}{3},-\dfrac{\pi}{3})\cup (\dfrac{\pi}{3},\dfrac{2\pi}{3})$

018438
$(1,3)$

023601
\begin{tikzpicture}[>=latex, scale = 0.6]
\draw [->] (-7,0) -- (7,0) node [below] {$x$};
\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\draw [domain = 0:2*pi,samples = 200] plot (\x,{sin(\x/pi*180)}) plot (-\x,{sin(\x/pi*180)});
\draw [dashed] (pi/2,0) --++ (0,1) -- (-pi/2,1) --++ (0,-1) (3*pi/2,0) --++ (0,-1) -- (-3*pi/2,-1) --++ (0,1);
\draw (0,1) node [below left] {$1$} (0,-1) node [below left] {$-1$};
\draw (pi/2,0) node [below] {$\frac{\pi}{2}$} (-pi/2,0) node [below] {$-\frac{\pi}{2}$};
\draw (3*pi/2,0) node [below] {$\frac{3\pi}{2}$} (-3*pi/2,0) node [below] {$-\frac{3\pi}{2}$};
\end{tikzpicture}

024726
$\dfrac{16}{65}$或$\dfrac{56}{65}$

040264
(1) $\dfrac 23 \pi$; (2) 顶角为$120^\circ$的等腰三角形

024727
$\dfrac{\sqrt{5}-1}{4}$