In this paper a novel method for angular position determination using sensors with sin/cos output and without an excitation signal, is presented. The linearization of the sensor transfer characteristic and digitalization of the measurement results are performed simultaneously with a goal to increase the measurement resolution. This improvement is particularly important for low angular velocities, and can be used to increase the resolution of incremental Hall, magnetic and optical sensors. This method includes two phases of sin/cos signal linearization. In the first linearization phase the pseudo-linear signal is generated. The second linearization phase, executed by the two-stage piecewise linear ADC, is an additional linearization of the pseudo-linear signal. Based on the LabVIEW software simulations of the proposed method, the contribution of each processing phase to a final measurement error is examined. After the proposed method is applied within $2{pi}$ [rad] range, the maximal nonlinearity is reduced from 0.3307 [rad] ($18.9447^{circ}$) to $3{cdot}10^{-4}$ [rad] ($0.0172^{circ}$).