Three new simple algorithms for generating random variates from the \(t\) distribution are presented: two independent ones and their combination. The combined algorithm is almost uniformly fast for all degrees of freedom \(\nu\). For the large \(\nu\) it works slightly slower than the method of \textit{R. W. Bailey} [Math. Comput. 62, No. 206, 779--781 (1994; Zbl 0805.65005)], especially, for \(\nu\) not far from 3; but it works appreciably faster than ``ratio of uniforms'' method in the version of \textit{L. Devroye} [Non-uniform random variate generation. New York etc.: Springer-Verlag (1986; Zbl 0593.65005), p.~201]. For the small \(\nu\) the first component of combined algorithm (generalization of the ``ratio of uniforms'' method for the Cauchy distribution) is a bit faster than Bailey's method.