Precise, wide-range approximations to arc sine function suitable for analog implementation in sensors and instrumentation applications

This paper presents four newly developed algebraic approximations of the inverse sine function, defined for the full [-1,+1] input range. These approximations contain few terms, and have numerical coefficients with low number of significant figures. The maximum absolute errors of the formulas range between 4.07×10^-4% and 5.64×10^-2% of the maximum value (i.e., π/2) returned by the arc sine function. These approximations are particularly suited to the determination of mechanical and electrical angles in sensors and instrumentation applications. One of the proposed expressions has been implemented using analog electronic circuitry. The converter built was successfully tested and characterized using both a PC-based test rig, and a commercial resolver. The theory, computer simulation and some experimental results are given.