<p>The precision measurement of capacitance necessitates the utilisation of a precision capacitance bridge, wherein a sine signal serves as a reference. Consequently, the precision of the sine signal is of paramount importance for the precision measurement of capacitance. In the conventional method of generating a sine signal, a look-up table is employed as the data source. However, the look-up table approach necessitates an excessive amount of read-only memory space to fulfil the requirements of high-precision scenarios. In this paper, we proposes an novel algorithm based on Taylor expansion to calculate the sine function. This algorithm doesn’t use any read-only storage space. Compared with the Coordinate Rotation Digital Computer algorithm in computer, it is based on the pipelined architecture to balance latency and digital signal processor resource consumption. For the Lagrange residual term error problem of Taylor expansion, the optimization algorithm using trigonometric periodicity and the complementary algorithm of sine and cosine functions is proposed. To evaluate the accuracy of the sine function generated by the algorithm, direct digital synthesis and digital to analog converter outputs are utilized to improve the accuracy and enhance the total harmonic distortion as compared to the conventional algorithm.</p>