The author has obtained summation of a number of trigonometric series by using various Fourier transforms contained in \textit{A. Erdélyi}, \textit{W. Magnus}, \textit{F. Oberhettinger} and \textit{F. G. Tricomi}: ``Tables of integral transforms'' Vol. I (1954; Zbl 0055.36401); Vol. II (1954; Zbl 0058.34103). For example, out of six theorems contained in this paper, Theorem 1 reads as follows: Let \(f(x)\) exist in \(0\leq x<\infty\) and let \(g_s(y)\) be the sine transform of \(f(x)\), i.e. \(g_s(y)=\int^\infty_0 f(x)\sin xy \,dx\). Then \[ \sum^ \infty_{k=1} g_s(k) \sin kt = \frac12 \left\{f(t)+\sum^\infty_{n=1}[f(2n\pi+t)-f(2n\pi- t)]\right\}\quad(0\leq t\leq 2\pi). \]