Trigonometric Resolution in Analog Computers by Means of Multiplier Elements

A method of generating sine and cosine functions in analog computers by means of multiplier elements and integrators is discussed. Static accuracy of the method is analyzed and found to be essentially equal to the accuracy of the multipliers employed. The system accepts dθ/dt as the input and generates output voltages of sinθ and cos θ. Amplitude-stabilizing loops are employed to maintain sin
²
θ+cos
²
θ = 1. Advantages of the method include representation of unlimited range in angles, dynamic capabilities far beyond that of the multipliers alone, and possibility of employing electronic multipliers. The method has been successfully used to compute Euler angles in analog computer solutions of the three-dimensional flight equations.