In this paper, the $arccos(cos^{-1})$ arithmetic unit for mobile graphics accelerator is designed. The mobile vector graphics applications need tight area, execution time, power dissipation, and accuracy constraints compared to desktop PC applications. The designed processor adopts 2nd-order polynomial approximation scheme based on IEEE floating point data format to satisfy speed and accuracy conditions and reduces area via hardware sharing structure. The arccosine processor consists of 15,280 gates and its estimated operating frequency is about 125Mhz at operating condition of $0.35{mu}m$ CMOS technology. Because the processor can execute arccosine function within 7 clock cycles, it has about 17 MOPS(million arccos operations per second) execution rate and can be applicable to mobile OpenVG processor. And because of its flexible architecture, it can be applicable to the various transcendental functions such as exponential, trigonometric and logarithmic functions via replacement of ROM and minor hardware modification.