Positioning of \flalign and arrows between the equation

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

\documentclass[12pt,parskip]{scrartcl}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{geometry}
\usepackage[english]{babel}
\selectlanguage{english}

\begin{document}
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;$\begin{minipage}[r]{8cm}
\begin{flalign*}
\beta_0
&=
\cos\left(\frac{\Phi}{2}\right)\longrightarrow&
\Phi
&=2\arccos\left(\beta_0\right)
=
118.67^\circ\\
\beta_1
&=
e_1\sin\left(\frac{\Phi}{2}\right)\longrightarrow&
e_1
&=
\frac{\beta_1}{\sin\left(\frac{\Phi}{2}\right)}
=
-0.857716\\
\beta_2
&=
e_2\sin\left(\frac{\Phi}{2}\right)\longrightarrow&
e_2
&=
\frac{\beta_2}{\sin\left(\frac{\Phi}{2}\right)}
=
-0.513132\\
\beta_3
&=
e_3\sin\left(\frac{\Phi}{2}\right)\longrightarrow&
e_3
&=
\frac{\beta_3}{\sin\left(\frac{\Phi}{2}\right)}
=
-0.031914
\end{flalign*}
\end{minipage}\\
\end{document}


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:

\documentclass[12pt,parskip]{scrartcl}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{alignat*}{3}
\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
\end{alignat*}
\end{document}


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:

\documentclass[12pt,parskip]{scrartcl}
\begin{document}
$\begin{array}{r@{{}={}}l@{\quad\longrightarrow\quad}r@{{}={}}l@{{}={}}l} \beta_0 & \cos(\frac{\Phi}{2}) & \Phi & 2\arccos(\beta_0) & 118.67^\circ \\ \beta_1 & e_1\sin(\frac{\Phi}{2}) & e_1 & \frac{\beta_1}{\sin(\frac{\Phi}{2})} & -0.857716 \\ \beta_2 & e_2\sin(\frac{\Phi}{2}) & e_2 & \frac{\beta_2}{\sin(\frac{\Phi}{2})} & -0.513132 \\ \beta_3 & e_3\sin(\frac{\Phi}{2}) & e_3 & \frac{\beta_3}{\sin(\frac{\Phi}{2})} & -0.031914 \end{array}$
\end{document}


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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