6830 



Plane Trigonometry. Formulas 



6830 



and cos (A B), demonstration. 



Rispal, A. N. A. Mth. 5 (1846) 84-. 

 deduced from triangle. Grunert, J. A. 



Grunert Arch. 21 (1853) 237-. 

 , generality of, demonstration. Spitz, 



C. Grunert Arch. 32 (1859) 293-. 

 , demonstration. Schreder, E. Grunert 



Arch. 36 (1861) 447-. 

 . Barbe, P. A. Cond. Pon. Chauss. 



9 (1865) 182-. 



deduced from Ptolemy's theorem. 

 Tucker, R. [1865] Mess. Mth. 3 (1866) 123. 



. Tucker, R. [1865] Mess. Mth. 4 



(1868) 31-. 

 . Lyetnikov, A. F. (xn) Bee. Mth. 



(Moscou) 2 (1867) (Pt. 2) 96-. 



. Lemonnier, H. N. A. Mth. 10 

 (1871) 26-. 



. Gravelaar, A. W. N. Arch. Wisk. 



5 (*1879) 187-. 

 . Zejliger, D. N. Kazan S. Ps.-Mth. 



Bll. 2 (1893) (Prot.) 23. 



, and other formulae, geometrical 

 demonstration. Butters, J. W. Edinb. 

 Mth. S. P. 15 (1897) 86-. 



- deduced from triangle. Bochow, . 



Arch. Mth. Ps. 17 (1900) 97-. 



Sin x = I*-*, n tfb r j"l^ . D U Bourguet, . 

 o TO 



Gergonne A. Mth. 3 (1812-13) 19-. 

 Sin"*0 and cos m in series of sines and 



cosines of multiples of 6. Pagani, G. M. 



Ferussac Bll. Sc. Mth. 5 (1826) 4-. 

 Sin m x and cos m x for all values of m. Gamier, 



J. G. Brux. Ac. Bll. 6 (1839) (pte. 2) 375-, 



488-. 

 Sinm0 and cosmB in terms of sin0 and cos#. 



Moon, R. Camb. Mth. J. 4 (1845) 250- . 

 Sinx and cos a;, imaginary expressions for. 



Y. Mathematician 1 (1845) 232-. 

 Sin (xy) or COS(XT/), simple demonstration. 



Astrand, J. J. Grunert Arch. 18 (1852) 479-. 

 Sin and cos . Sturm, J. B. Grunert 



Arch. 24 (1855) 112-. 



Sin"0 and cos n 0, expansion in sines and 

 cosines of multiples of 0. Wolfers, J. P. 

 Grunert Arch. 24 (1855) 303-. 



Sin - , - , - , etc. , and cos , etc. Gerono, G. C. 



N. A. Mth. 17 (1858) 46-. 

 Sin(0 + J + a + ... + n ) and cos (9 + ... + 6J, 



expansion, and related theorem of numbers. 



Unferdinger, F. Grunert Arch. 34 (1860) 72-. 

 Sin fj.9 and cos /j.6, expansion. Gylden,H. As. 



Nr. 69 (1867) 193 -. 

 Sin (na + z), and cos (na + z), sin a, and cos n a, 



expansion. Andre, D. N. A.Mth.lO(1871)359-. 

 Sin (A +B + ...) or cos (A + B + ...). Legge, A. 



di. G. Mt. 9 (1871) 377-. 

 Sin oo and cos OD . Walton, W. QJ. Mth. 11 



(1871) 326-. 

 Sin- 1 and cos" 1 (x + iy), values. Schlomilch, 0. 



Z. Mth. Ps. 17 (1872) 245-. 

 Sin no. and cos wo, expansion in powers of 



2 cos a and 2 sin a. Le Besgue, V. A. N. A. 



Mth. 12 (1873) 425-. 



Sin ma and cos?a in terms of sin a or cos a. 



Mourgue, . N. A. Mth. 12 (1873) 408-. 

 , calculation. 



Ocagne, M. d\ N. Arch. Wisk. 17 (1890) 



229-. 

 lsin(2|3 + l) u. Cayley, A. Mess. Mth. 5 



(1876) 7-. 



sin0 sin 20 sin 30 

 2 ~~p" 2 ' 3 ' g enera l ls ation. 



Stormer, C. Acta Mth. 19 (1895) 341-. 

 Tan (A 1 + A 2 + etc.) in terms of tan^ 1; tan A 2 , 



etc., demonstration. Stainville, de. Par. 



EC. Pol. Cor. 2 (1809-13) 432-. 

 Tan z, continued fraction for. Schlomilch, O. 



Z. Mth. Ps. 16 (1871) 259-. 

 Tan nx, continued fraction for. Glaisher, 



J. W. L. [1873-74] (vn) Mess. Mth. 3 



(1874) 137; (x) 4 (1875) 65-. 



Tan ( So, ), tan n0, and other formulae. An- 



glin, A . H. [1884] Ir. Ac. P. 4 (1884-88) 259-. 

 Sarc tana r . Anglin, A. H. Arch. Mth. Ps. 2 

 1 (1885) 407-. 

 = ncot. ( J, sign. Stern, M. A. 



Liouv. J. Mth. 5 (1840) 216-. 



b + c , B+C I , B-C 



:- = tan jr / tan - , geometric demon- 

 stration. Vignal, . N. A. Mth. 3 (1844) 

 456-. 



Foundations of trigonometry. Brisse, C. N. A. 



Mth. 16 (1877) 49-. 

 Functions, developments and properties. 



Gamier, J. G. Quetelet Cor. Mth. 11 



(1839) 283-. 

 Goniometry. Lindman, C. F. Arch. Mth. Ps. 



53 (1871) 112-. 



, problem. Cotterill, T. [1865] QJ. Mth. 7 

 (1866) 259-. 



, (Cotterill). Cayley, A. QJ. Mth. 15 

 (1878) 196-. 



, theorems. Schlomilch, O. Grunert Arch. 

 8 (1846) 453-; 9 (1847) 1-. 



Graphic tables, use in solution of problems in 



cosmography and spherical trigonometry. 



Collignon, E. N. A. Mth. 18 (1879) 



179- ; 1 (1882) 490-. 

 History. Suter, H. Bb. Mth. (1893) 1-. 

 Identities, algebraic, in plane trigonometry. 



Meyer, W. F. Fschr. Mth. (1898) 441. 



, trigonometrical. Fouret, G. N. A. Mth. 

 2 (1883) 262-. 



Identity. Hermite, C. N. A. Mth. 4 (1885) 57-. 



, case. Glaisher, J. W. L. As. Fr. C. B. 9 

 (1880) 222-. 



involving products of four sines. Glaisher, 

 J. W. L. B. A. Ep. (1880) 484-. 



, arc tan - = S arc tan where 



A j a 



Glaisher, J. W. L. [1877-78] As. Fr. C. B. 6 

 (1877) 211- ; QJ. Mth. 15 (1878) 151- ; 16 

 (1879) 329-. 



465 



