Plane trigonometry, by S.L. Loney.

DE MOIVRE'S THEOREM. 319 27r + 0 27r + 0 cos -- +/ - sin47r + 0. 47T + 0 cos --- + /- 1 sin q q 67r /. 67+r + cos -- + -1 sin --............(1), q q is equal to one of the values of (cos 0 + -1 sin O)q. The highest value that we need assign to n is q-1; for the values q, q + 1, q + 2,... will be found to give the same result as the values 0, 1, 2,.... Also no two of the quantities (1) will be the same. For all the angles involved therein differ from one another by less than 27r and no two angles, differing by less than 27r, have their cosines the same and also their sines the same. To sum up; By giving to n the successive values 0, 1, 2,... q- 1 in the expression 2n7r + 0. 2nr + 0 cos J+ /-1 sin q q we obtain q, and only q, different values for 1 (cos 0 + d/ —1 sin 0). 271. By the use of the last article we can now obtain trigonometrical expressions for any root of a quantity of the form x + yi.

/ 534
Pages

Actions

file_download Download Options Download this page PDF - Pages 317-336 Image - Page 317 Plain Text - Page 317

About this Item

Title
Plane trigonometry, by S.L. Loney.
Author
Loney, Sidney Luxton, 1860-
Canvas
Page 317
Publication
Cambridge [Eng.]: University press,
1893.
Subject terms
Plane trigonometry.

Technical Details

Link to this Item
https://name.umdl.umich.edu/abn7298.0001.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/abn7298.0001.001/343

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:abn7298.0001.001

Cite this Item

Full citation
"Plane trigonometry, by S.L. Loney." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/abn7298.0001.001. University of Michigan Library Digital Collections. Accessed May 2, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.