A parameter $\lambda$ is called a Misiurewicz parameter in the tangent family if a post-singular set of a map $\lambda\tan z$ is a bounded, hyperbolic repelling set. During my talk I will present a comparison of properties of Misiurewicz parameters in the tangent family and the other families of maps, I will also give simplest examples. I will show that in the tangent family Misiurewicz parameters are accumulation points of hyperbolic parameters.