Deducing the Approximate Formula of Arch Field Area by Making Use of Taylor Series

Taylor series is an important tool for approximate calculation in Calculus.In order to solve the precision problem of approximate calculation of arch field area that we often meet with in the projects of construction and decoration,we obtain the approximate calculation formula of arch field area by using Taylor series of function.When the central angle is between 0°and 150°,the precision of result can be controlled under 2‰.Furthermore,we get four approximate calculation formulas for different central angles.By analysing their relative errors,we get a relative error form for the four formulas.Based on different construction precision requirements,we can choose different formulas to calculate by using the form.