Cost function based routing has been widely studied in wireless sensor networks for energy efficiency improvement and network lifetime elongation. However, due to the complexity of the problem, existing solutions have various limitations. In this paper, we analyze the inherent factors, design principles and evaluation methods for cost function based routing algorithms. Two energy aware cost based routing algorithms named Exponential and Sine Cost Function based Route (ESCFR) and Double Cost Function based Route (DCFR) have been proposed in this paper. For ESCFR, its cost function can map small changes in nodal remaining energy to large changes in the function value. For DCFR, its cost function takes into consideration the end-to-end energy consumption, nodal remaining energy, resulting in a more balanced and efficient energy usage among nodes. The performance of the cost function design is analyzed. Extensive simulations demonstrate the proposed algorithms have significantly better performance than existing competing algorithms.