In the coordinate plane,the graps of functions $y=sin x$ and $y=tan x$ are drawn, along with the coordinate axes. Using compass and ruler, construct a line tangent to the graph of sine at a point above the axis, $Ox$, as well at a point below that axis (the line can also meet the graph at several other points)
1. **Identify the Tangent Line Equation:**
   The tangent line to the graph of \( y = \sin x \) at a point \( t \) is given by:
   \[
   y = x \cos t + \sin t - t \cos t
   \]
   This equation is derived from the point-slope form of the tangent line, where the slope at \( t \) is \( \cos t \) and the point of tangency is \( (t, \sin t) \).

2. **Condition for Double Tangency:**
   For the line to be tangent to the graph of \( \sin x \) at two distinct points \( t_1 \) and \( t_2 \), the slopes at these points must be equal and non-zero:
   \[
   \cos t_1 = \cos t_2 \neq 0
   \]
   Additionally, the y-intercepts of the tangent lines at these points must be equal:
   \[
   \sin t_1 - t_1 \cos t_1 = \sin t_2 - t_2 \cos t_2
   \]

3. **Simplifying the Condition:**
   Since \( \cos t_1 = \cos t_2 \), we have:
   \[
   \sin t_1 = -\sin t_2
   \]
   This implies that \( t_2 = 2k\pi - t_1 \) for some integer \( k \). Substituting this into the y-intercept condition, we get:
   \[
   \sin t_1 - t_1 \cos t_1 = -\sin t_1 - (2k\pi - t_1) \cos t_1
   \]
   Simplifying, we find:
   \[
   t_1 - k\pi = \tan t_1
   \]

4. **Constructing the Tangent Line:**
   - Mark the point \( M(0, 2\pi) \) as the second nonzero intersection of \( \sin x \) with the x-axis.
   - Using a compass centered at \( (0,0) \) and the point \( M \), mark the point \( N(0, -2\pi) \).
   - With a ruler, draw the line \( MN \) (equation \( y = x - 2\pi \)).
   - Mark the intersection \( P \) of this line with the graph of \( \tan x \) between \( \frac{\pi}{2} \) and \( \pi \).
   - Using a compass and ruler, construct the symmetric point \( P' \) of \( P \) relative to the x-axis.
   - Using a compass and ruler, draw the line \( x = 2\pi \).
   - Using a compass and ruler, construct the symmetric point \( Q \) of \( P \) relative to the line \( x = 2\pi \).
   - Using a compass and ruler, construct the symmetric point \( Q' \) of \( P' \) relative to the line \( x = 2\pi \).
   - The line \( PP' \) intersects the graph of \( \sin x \) at point \( A \).
   - The line \( QQ' \) intersects the graph of \( \sin x \) at point \( B \).
   - The line \( AB \) is the required double tangent.

The final answer is the line \( \boxed{ AB } \) is one suitable required double tangent.