The electrodynamics eigenmodes boundary problem for sectoral coaxial single-ridged waveguides is solved by the integral equation technique utilizing the introduced system of orthogonal basis functions, which correctly take into account the singular field behavior at the ridge. The analysis of the dependence of cutoff wave numbers convergence on the type and the amount of basis functions has been carried out. It is shown that for obtaining residual error less than 0,1 % it is necessary to utilize in two times more unorthogonal basis functions, which correctly take into account singularity at the ridge, than introduced orthogonal basis functions, which correctly take into account singularity at the ridge, and in five times more orthogonal trigonometric basis functions, which don't take into account singularity at the ridge. Besides the computing time increases in 4 and in 20 times, respectively.