“He gave an example of a trigonometric series which diverged at every point, yet its coefficients tended to zero.”

“He summed series, and discovered addition theorems for trigonometric and hyperbolic functions using the differential equations they satisfy.”

“From this he was able to prove that if a function was representable by a trigonometric series then this series is necessarily its Fourier series.”

“Rather than using geometrical methods, as Ptolemy had done, al-Battani used trigonometrical methods which were an important advance.”

“Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research.”

“Seaton threw down the papers and picked up his slide-rule, a twenty-inch trigonometrical duplex.”