 | William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray (IV), Rowland Edmund Prothero (Baron Ernle), George Walter Prothero - English literature - 1811 - 622 pages
...with the inquiries relating to Physical Astronomy. 4. On the Sine and Cosine of the Multiple Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant. 5. On Magic squares. 6. An account of an Experiment for... | |
 | Thomas Leybourn - Mathematics - 1814 - 420 pages
...frsK»"*) (a cos , } = i ^ (2COSX)"— " I will add here what appears to be a very simple method of finding the sine and cosine of an arc, in terms of the arc itself: it does not require the use of fluxions. With respect to the form of series to be assumed, there is... | |
 | William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray (IV), Rowland Edmund Prothero (Baron Ernle), George Walter Prothero - English literature - 1820 - 594 pages
...with the inquiries relating to Physical Astronomy-. 4. On the Sine and Cosine of the Multiple Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and & new Theorem fof the Elliptic Quadrant. 5. On Magic squares. 6 An nccount of an Experiment for... | |
 | Dionysius Lardner - Geometry, Algebraic - 1823 - 658 pages
...these equations may be deduced all the other formulae of trigonometry. We can find expressions for the sine and cosine of an arc in terms of the arc itself from the same formulae by adding and subtracting the equations cos. x + л/ — 1 sin. x = e* ~l, cos.... | |
 | Dionysius Lardner - Geometry, Algebraic - 1831 - 582 pages
...these equations may be deduced all the other formulae of trigonometry. We can find expressions for the sine and cosine of an arc in terms- of the arc itself from the same formulae by adding and subtracting the equations cos. x + V — 1 sin. x = t* , cos.... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...2>cos ,_3 A sin.3A • * M + &C. From these two expressions may be obtained series, for the value of the sine and cosine of an arc in terms of the arc itself. For let n = — , and sin. A = 0 = A, then nA t= — = any finite quantity x; hence by these substitutions... | |
 | Siméon Denis Poisson - 1842 - 706 pages
...sin«> by expanding cos.(te sin u), sin.(tesinu) into a series according to the formula expressing the sine and cosine of an arc in terms of the arc, we will obtain the expression for cos (tu — te sinu) given in the text. (h) By substituting for r... | |
 | James Bates Thomson - Plane trigonometry - 1844 - 148 pages
.....~*' When 6 is negative, the signs of these roots are to be changed. 225. To find series' expressing the sine and cosine of an arc in terms of the arc itself, divide both members of (229) and (230) by cos- A, and the terms in the second members, exclusive of... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 pages
...— B) = 2 cos A . cos B ... (3) , (A - B) - ( cos (A — B) — cos (A + B)= 2 sin A . sin u ... (4) 28. To find the sine and cosine of an arc in terms of the sine of double the arc. cos8 A + sin2 A = 1 2 sin A . cos A = sin 2 A ; .'. by addition and subtraction,... | |
 | James Hann - Plane trigonometry - 1854 - 140 pages
...sine and cosine in a series. From equations (5) and (6), Euler has deduced the series which expresses the sine and cosine of an arc in terms of the arc itself. Retaining the supposition that n is a whole number, we can dispose of ф in such a manner that пф... | |
| |
Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant. 
