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I want to have something as following, but I'm not satisfied with the result:




Sorry for the bad formatting, I am still a beginner in LaTex. I would like to connect the equations with arrows, but the arrows should also be aligned. And the equations should be close together... I tricked with a minipage, but I think that is also not the best solution. Thank you!

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You could use alignat to align at multiple positions:

enter image description here

\usepackage{amsmath}% http://ctan.org/pkg/amsmath
  \beta_0 &= \cos(\tfrac{\Phi}{2}) && \longrightarrow\ & \Phi &=2\arccos(\beta_0)=118.67^\circ \\
  \beta_1 &= e_1\sin(\tfrac{\Phi}{2}) && \longrightarrow\ & e_1 &=\frac{\beta_1}{\sin(\tfrac{\Phi}{2})}=-0.857716 \\
  \beta_2 &= e_2\sin(\tfrac{\Phi}{2}) && \longrightarrow\ & e_2 &=\frac{\beta_2}{\sin(\tfrac{\Phi}{2})}=-0.513132 \\
  \beta_3 &= e_3\sin(\tfrac{\Phi}{2}) && \longrightarrow\ & e_3 &=\frac{\beta_3}{\sin(\frac{\Phi}{2})}=-0.031914

Consider reading Herbert Voss' mathmode document. Specifically section 25 align environments (p 43 onward).

Alignment using a standard array is also possible. Here's one such suggestion:

enter image description here

    \beta_0 & \cos(\frac{\Phi}{2})    & \Phi & 2\arccos(\beta_0) & 118.67^\circ \\
    \beta_1 & e_1\sin(\frac{\Phi}{2}) & e_1 & \frac{\beta_1}{\sin(\frac{\Phi}{2})} & -0.857716 \\
    \beta_2 & e_2\sin(\frac{\Phi}{2}) & e_2 & \frac{\beta_2}{\sin(\frac{\Phi}{2})} & -0.513132 \\
    \beta_3 & e_3\sin(\frac{\Phi}{2}) & e_3 & \frac{\beta_3}{\sin(\frac{\Phi}{2})} & -0.031914

The use of @{{}={}} inserts = between the array cells as a "column separator", but also makes sure that the spacing matches that of a regular binary relation.

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