I came across this system of trigonometric equations inbetween a problem in Numerical Linear Algebra.
I was required to find $p^2$ and $\cos(\theta)$ in terms of $q^{(k-1)},q^{(k)},q^{(k+1)},q^{(k+2)}$ where $k$ represents the $k^\mathrm{th}$ iteration.
$q^{(k-1)}=Cp^{k-1}\cos((k-1)\theta+\phi)$
$q^{(k)}=Cp^{k}\cos((k)\theta+\phi)$
$q^{(k+1)}=Cp^{k+1}\cos((k+1)\theta+\phi)$
$q^{(k+2)}=Cp^{k+2}\cos((k+2)\theta+\phi)$
Here $Cp^n$ means a scalar "C" multiplied with the $n^{th}$ power of the scalar $p$
I would highly appreciate any help