The Intel 8087, introduced in 1980, significantly accelerated floating-point operations in computers, including the IBM PC. A recent analysis of the chip's circuitry and microcode has shed light on the algorithm behind its tangent instruction, known as FPTAN. Unlike other approaches that rely solely on CORDIC or polynomial approximation, the 8087 combines these methods to achieve high accuracy and performance, enabling it to compute a tangent in 90 microseconds, a substantial improvement over the 13,000 microseconds required by the 8086 microprocessor. By reverse-engineering the chip, the complex algorithm used to calculate the tangent function has been revealed, providing insight into the innovative design of this influential floating-point processor.