A Bayesian procedure for analyzing longitudinal binary responses using a periodic cosine function was developed. It was assumed that, after adjustment for "seasonal" effects, the oscillation of the underlying latent variables for longitudinal binary responses was a stationary series. Based on this assumption, a single dimension sinusoidal analysis of longitudinal binary responses using the Gibbs sampling and Metropolis algorithms was implemented in a study of clinical mastitis records of Norwegian Red cows taken over five lactations.