Abstract We study the dynamics of a meromorphic perturbation of the family λ sin z \lambda \sin z by adding a pole at zero and a parameter μ \mu , that is, f λ , μ ( z ) = λ sin z + μ / z {f}_{\lambda ,\mu }\left(z)=\lambda \sin z+\mu \hspace{-0.08em}\text{/}\hspace{-0.08em}z , where λ , μ ∈ C ⧹ { 0 } \lambda ,\mu \in {\mathbb{C}}\hspace{-0.16em}\setminus \hspace{-0.16em}\left\{0\right\} . We study some geometrical properties of f λ , μ {f}_{\lambda ,\mu } and prove that the imaginary axis is invariant under f n {f}^{n} and belongs to the Julia set when ∣ λ ∣ ≥ 1 | \lambda | \ge 1 . We give a set of parameters ( λ , μ ) \left(\lambda ,\mu ) , such that the Fatou set of f λ , μ {f}_{\lambda ,\mu } has two super-attracting domains. If λ = 1 \lambda =1 and μ ∈ ( 0 , 2 ) \mu \in \left(0,2) , the Fatou set of f 1 , μ {f}_{1,\mu } has two attracting domains. Also, we give parameters λ , μ \lambda ,\mu such that ± π / 2 \pm \pi \hspace{-0.08em}\text{/}\hspace{-0.08em}2 are fixed points of f λ , μ {f}_{\lambda ,\mu } and the Fatou set of f λ , μ {f}_{\lambda ,\mu } contains attracting domains, parabolic domains, and Siegel discs, we present examples of these domains. This paper closes with an example of f λ , μ {f}_{\lambda ,\mu } , where the Fatou set contains two types of domains, for λ , μ \lambda ,\mu given.