An autonomous humanoid robot (HR) with learning and control algorithms is able to balance itself during sitting down, standing up, walking and running operations, as humans do. In this study, reinforcement learning (RL) with a complete symbolic inverse kinematic (IK) solution is developed to balance the full lower body of a three-dimensional (3D) NAO HR which has 12 degrees of freedom. The IK solution converts the lower body trajectories, which are learned by RL, into reference positions for the joints of the NAO robot. This reduces the dimensionality of the learning and control problems since the IK integrated with the RL eliminates the need to use whole HR states. The IK solution in 3D space takes into account not only the legs but also the full lower body; hence, it is possible to incorporate the effect of the foot and hip lengths on the IK solution. The accuracy and capability of following real joint states are evaluated in the simulation environment. MapleSim is used to model the full lower body, and the developed RL is combined with this model by utilizing Modelica and Maple software properties. The results of the simulation show that the value function is maximized, temporal difference error is reduced to zero, the lower body is stabilized at the upright, and the convergence speed of the RL is improved with use of the symbolic IK solution.