...cos. 2 A — cos. 2 A &e. 'fec. J (29.) The sines and cosines of multiple arcs may also be developed in terms of the powers of the sine and cosine of the simple arc, by help of a remarkable formula, known by the name of De Moivre's formula, which may be easily established,...

...ЗА cos. 2 A — cos.2A Ac. Ac. J (29.) The sines and cosines of multiple arcs may also be developed in terms of the powers of the sine and cosine of the simple are, by help of a remarkable formula, known by the name' of De Moivre's formula, •which may be easily...

...po.wers of the roots of the equation л? — .r+p=0, we may deduce the trigonometrical series for the cosine of the multiple arc in terms of the powers of the cosine of the simple arc in the following' manner: — Let p = - in the preceding equation, of which'the...

...of these formulae, the sines and cosines of the multiple angles, 2 A, 3 A, 4 A .... can be expressed in terms of the powers of the sine and cosine of the angle A. a. For, if in formula!., n = 2, sin. 2 A = 2 sin. A cos. A. If Я = 3, Sin. 3 A + ein.A =...

...cos.'"a. By these formulas, for sln.ma, and cos. от«, we find the values of the sines and cosines of the multiple arc in terms of the powers of the sine and cosine of the simple arc; and the expression for the tangent ma is the tangent of the multiple arc in terms of the powers of...

...squares. Camb. Math. Journ. IV., 1845, pp. 209-214. 7. On a new method of obtaining the expression for the sine and cosine of the multiple arc in terms of the like functions of the simple arc. Camb. Math. Journ. IV., 1845, pp. 250252. 8. On FRESNEL'S theory...