The simplest approach is to use a phantom where a sign is missing; \mathbin{\phantom{-}} will behave exactly like - in all situations, as far as spacing is concerned, but printing nothing.
\documentclass{article}
\usepackage{amsmath}
% first strategy
\newcommand{\nm}{\mathbin{\phantom{-}}}
% second strategy
\begingroup\lccode`~=``\lowercase{\endgroup\def~}{\mathbin{\phantom{-}}}
\AtBeginDocument{\mathcode``="8000 }
\begin{document}
\begin{equation}
\begin{split}
\cos(x) &= c_1 + c_2x^2 + c_3x^4 \\
&= c_1 + x^2(c_2 + c_3x^2) \\
\text{where} \\
c_1 &= \nm 0.99940307 \\
c_2 &= - 0.49558072 \\
c_3 &= \nm 0.03679168
\end{split}
\end{equation}
\begin{equation}
\begin{split}
\cos(x) &= c_1 + c_2x^2 + c_3x^4 \\
&= c_1 + x^2(c_2 + c_3x^2) \\
\text{where} \\
c_1 &= `0.99940307 \\
c_2 &= -0.49558072 \\
c_3 &= `0.03679168
\end{split}
\end{equation}
\end{document}
The first strategy is simpler from a programming point of view; for the second I used a character that's not commonly used in math and made it “math active” expanding to the same phantom as in \nm.

c_1 &= \hphantom{-}0.99940307? – GuM Sep 26 '18 at 22:15alignand thesplitenvironments, and that\text{where}should probably be\intertext{where}. I advise you to have a look at the manual of theamsmathpackage: on a TeXLive installation, it can be brought up by typingtexdoc amsmathat a shell prompt. – GuM Sep 26 '18 at 22:28\shortintertext{where}might be better with themathtoolspackage. – Peter Grill Sep 26 '18 at 23:08