In the early 2000s, the geometry of a one-parameter family of generalized complex number systems was studied (Math. Mag. 77(2)(2004)). This family is denoted by Cp. It is well known that Cp matches up with the elliptical complex number system when p is any negative real number. By using this system, Özen and Tosun expressed the elliptical complex valued trigonometric functions cosine, sine and p-trigonometric functions p-cosine, p-sine (Adv. Appl. Clifford Algebras 28(3)(2018)). In this study, we introduce the remained elliptical complex valued trigonometric and p-trigonometric functions. Also we define the corresponding single-valued principal values of the inverse trigonometric and p-trigonometric functions by following the similar steps given in the literature.