The Power Series and the Infinite Products for sin x and cos x

H. S. Carslaw

doi:10.2307/3605604

The Power Series and the Infinite Products for sin x and cos x

Published online by Cambridge University Press: 03 November 2016

H. S. Carslaw

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1. The course of Plane Trigonometry “up to and including the solution of triangles and the properties of the circles associated with a triangle” offers little difficulty to the teacher and no serious difficulty to the pupil. But in the further development of the subject, when the circular functions sin x, cos x, … are regarded as functions of the real variable x, the position is different.

Type: Research Article
Information: The Mathematical Gazette , Volume 15 , Issue 206 , March 1930 , pp. 71 - 77

DOI: https://doi.org/10.2307/3605604 [Opens in a new window]
Copyright: Copyright © Mathematical Association 1930

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page 71 note * Cf. Bromwich, Infinite Series (2nd ed.), § 59.

page 72 note * If u_n >a and lim u_n exists, then lim u_n ≧a.

page 72 note † This theorem was given by J. Tannery in his Introduction à la Théorie des Fonctions d’uns Variable (2e éd, Paris, 1904), p. 292. See Bromwich, loc. cit., § 49.

page 74 note * This can be proved easily by the Differential Calculus; and a proof without the Calculus is to be found in Hobson’s Plane Trigonometry (7th ed.), p. 128.

page 74 note † We know that