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Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant.
Key to System of practical mathematics. 2 pt. No.xvii - Σελίδα 139
των Scottish school-book assoc - 1845
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## The Quarterly Review

...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...

## New Series of The Mathematical Repository, Τόμος 3

Thomas Leybourn - 1814
...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...

## The Quarterly Review

...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...

## A System of Algebraic Geometry, Τόμος 1

Dionysius Lardner - 1823
...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....

## Treatise on Algebraic Geometry

Dionysius Lardner - 1831 - 512 σελίδες
...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....

## Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - 1833 - 208 σελίδες
...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...

## A treatise of mechanics, tr., and elucidated with notes, by H.H. Harte, Τόμος 1

Siméon Denis Poisson - 1842
...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...

## Elements of Plane and Spherical Trigonometry: With the First Principles of ...

James Bates Thomson - 1844 - 126 σελίδες
.....~*' 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...

## Principles of geometry, mensuration, trigonometry, land-surveying, and ...

...— 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,...

## The Elements of Plane Trigonometry

James Hann - 1854 - 119 σελίδες
...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...