The coordinate rotation digital computer (CORDIC) algorithm is a broadly used iterative method for computing numerous mathematical functions, particularly trigonometric, hyperbolic, and vector rotations, without the requirement for multiplication operations. Instead, it employs iterative additions and bit-shifting, making it efficient for hardware implementation. However, a foremost limitation in conventional CORDIC designs lies in the gain compensation process, which leads to hardware complexity and accuracy trade-offs. Two novel methods are proposed to address these challenges: (1). The gain compensation is restructured at the input level rather than being applied iteratively or introduced in the final stage. This modification results in substantial performance improvements, including 59.4% error reduction, 6% area reduction, and 42% power reduction, effectively balancing computational complexity and precision. (2) A lookup table (LUT)-based technique is introduced, wherein precomputed gain values are stored for a fixed number of iterations. This method excludes the need for square root computations and iterative gain adjustments, thereby enhancing hardware efficiency. Related to existing approximation techniques, the LUT-based method achieves 50% error reduction, 75% area reduction, and 6% power reduction. Both solutions advance CORDIC implementation by significantly reducing computational error, area, and power consumption, making them highly suitable for modern low-power, high-performance digital signal processing systems.