We present results on

B \to J / ψ K π

decays using

e^{+} e^{-}

annihilation data collected with the BABAR detector at the

Υ (4 S)

resonance. The detector is located at the PEP-II asymmetric-energy storage ring facility at the Stanford Linear Accelerator Center. Using approximately

88 \times 10^{6}

B \bar{B}

pairs, we measure the decay amplitudes for the flavor eigenmodes and observe strong-phase differences indicative of final-state interactions with a significance of 7.6 standard deviations. We use the interference between the

K π

S

-wave and

P

-wave amplitudes in the region of the

K^{*} (892)

to resolve the ambiguity in the determination of these strong phases. We then perform an ambiguity-free measurement of

\cos ﻿ 2 β

using the angular and time-dependent asymmetry in

B \to J / ψ K^{* 0} (K_{S}^{0} π^{0})

decays. With

\sin ﻿ 2 β

fixed at its measured value and

\cos ﻿ 2 β

treated as an independent parameter, we find

\cos ﻿ 2 β = {2.72}_{- 0.79}^{+ 0.50} (s t a t) \pm 0.27 (s y s t)

, determining the sign of

\cos ﻿ 2 β

to be positive at 86% C.L.

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