Changing the angle of the vertical and horizontal axis of Sine curve 
Suppose we have $f(x)=\sin{(x)}$

The plot of $f(x)$ :


Suppose I want to modify the graph by :


*

*Changing the angle of horizontal axis: (Plane rotation...so both horizontal and the vertical axis changes)




How to achieve this? I mean the whole graph will look tilted say at an angle $\theta$...



*Changing the angle of vertical axis: (I guess it is called vertical axis!)




Again, how to achieve this? I mean the whole graph will kind of look italicized at an angle $\phi$...[Keeping the horizontal axis same] 



Hence, my question is how to achieve this rotation and tilt of $\sin(x)$.By 'achieve' I mean the new equations. I guess there will be a general formula too for almost all $f(x)$.

EDIT 
Also what will happen to the 1st question if the $z$-axis is involved (Revolution of that graph). That is how can i also revolve the curve along z axis?
BTW please give the new "equations" too along with "how-to-do" coz some examples help also along with the hints
P.S. - I know that after these transformations the curve may not remain a function but i still want the equations please!
Thanks
 A: Only addressing Q#2, italicizing:

          


The result above was achieved by multiplying by the 
shear matrix
below, with $\phi=30^\circ$:
$$
M = \left(
\begin{array}{ccc}
 1 & \tan (\phi )  \\
 0 & 1  \\
\end{array}
\right)
$$
For $\phi=60^\circ$:

          


If you parametrize the sine-curve as $(t, \sin (t))$, then multiplying by
the shear matrix results in
$$
M \cdot (\; t,\; \sin (t) \;) = \left( \; t + \sin (t) \tan (\phi ), \; \sin(t) \; \right) \;.
$$


This figure from Wikipedia (employing homogenous coordinates, and so $3 \times 3$ matrices) may help.
I used the "Shear in the $x$-direction" matrix:

          

A: There is a method to rotate a graph, that is, using the general rotation matrix, however, there is no general method, lets say $M$, such that $M(f(x))=f(x)_\phi$, since a counterexample holds, assuming $f(x)$ is not monotonic on interval $[a,b]$:
Say that $f(x_1)=f(x_2) = y_1$ when $x_1 < x_2$, a tilt of 90° will guarantee that $f(y_1)_\phi = x_1 = x_2$, so $f_\phi$ is not a function.
