Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 páginas |
Dentro del libro
Resultados 1-5 de 29
Página 18
... cos b cos c + sin b sin c cos A , cos b = cos c cos a + sin c sin a cos B , cos c = cos a cos b + sin a sin b cos C. These may be considered as the fundamental equations of Spheri- 18 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... cos b cos c + sin b sin c cos A , cos b = cos c cos a + sin c sin a cos B , cos c = cos a cos b + sin a sin b cos C. These may be considered as the fundamental equations of Spheri- 18 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Página 19
... equations of Spheri- cal Trigonometry ; we shall proceed to deduce various formulæ from them . 40. To express the sine of an angle of a spherical triangle in terms of the sides . We have COS A = cos a- cosb cos c ; sin b sin c cos a cos ...
... equations of Spheri- cal Trigonometry ; we shall proceed to deduce various formulæ from them . 40. To express the sine of an angle of a spherical triangle in terms of the sides . We have COS A = cos a- cosb cos c ; sin b sin c cos a cos ...
Página 21
... equation ; cos a = ( cos a cos b + sin a sin b cos C ) cos b + by transposition sin a sin b cos A sin C ; sin A cos a sin3 b = sin a sin b cos b cos C + sin a sin b cot A sin C ' ; divide by sin a sin b ; thus cot a sin b = cos b cos C ...
... equation ; cos a = ( cos a cos b + sin a sin b cos C ) cos b + by transposition sin a sin b cos A sin C ; sin A cos a sin3 b = sin a sin b cos b cos C + sin a sin b cot A sin C ' ; divide by sin a sin b ; thus cot a sin b = cos b cos C ...
Página 26
... equation ( 4 ) of the preceding article , cos ( a - b ) and C cot are necessarily positive quantities ; hence the equation . 2 shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus ( A + B ) and 4 ( a + b ) are either ...
... equation ( 4 ) of the preceding article , cos ( a - b ) and C cot are necessarily positive quantities ; hence the equation . 2 shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus ( A + B ) and 4 ( a + b ) are either ...
Página 30
... equations used are universally true . EXAMPLES . 1. If A = a , shew that B and b are equal or supplemental , as also C and c . 2. If one angle of a triangle be equal to the sum of the other two , the greatest side is double of the ...
... equations used are universally true . EXAMPLES . 1. If A = a , shew that B and b are equal or supplemental , as also C and c . 2. If one angle of a triangle be equal to the sum of the other two , the greatest side is double of the ...
Otras ediciones - Ver todo
Términos y frases comunes
a+b+c angular points approximately bisecting calculated centre circle described circular measure cos b cos cos² cos³ cosb cosines Crown 8vo deduce denote equal equation Fcap Fellow of St formed formulæ given greater Hence inscribed John's College late Fellow less Let ABC limp cloth lune M.A. Fellow middle point Napier's analogies Napier's Rules obtain perpendicular plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle quadrant radius regular polyhedron respectively right angles right-angled triangles School Second Edition Sermons preached shew shewn Similarly sin b sin sin² sin³ sine small circle solid angle solution sphere spherical excess spherical triangle Spherical Trigonometry St John's College suppose surface tangent tetrahedron Third Edition Treatise triangle ABC Trinity College University of Cambridge values vols
Pasajes populares
Página 26 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Página 26 - If two triangles have two sides of the one equal to two sides of the...
Página 16 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
Página 18 - Prize Essay for 1877. 8vo. &r. 6d. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
Página 14 - Crown 8vo. cloth, 6s. 6d. MORSE.— Working for God, and other Practical Sermons. By FRANCIS MORSE, MA Incumbent of St. John's, Ladywood, Birmingham. Second Edition. Fcap. 8vo.
Página 9 - THE ROMAN AND THE TEUTON. A Series of Lectures delivered before the University of Cambridge.
Página 11 - Extra fcap. 8vo. 4s. 6d. LATHAM. — The Construction of Wrought-iron Bridges. Embracing the Practical Application of the Principles of Mechanics to Wrought-iron Girder Work. By JH LATHAM, Civil Engineer. 8vo. With numerous detail Plates. Second Edition. [Preparing. LATHAM. — Black and White : A Three Months
Página 6 - THE GOLDEN TREASURY OF THE BEST SONGS AND LYRICAL POEMS IN THE ENGLISH LANGUAGE. Selected and arranged, with Notes, by FRANCIS TURNER PALGRAVE.
Página 135 - ANSTIE. — Stimulants and Narcotics, their Mutual Relations, With Special Researches on the Action of Alcohol, ^Ether, and Chloroform on the Vital Organism. By FRANCIS E. ANSTIE, MDMRCP 8vo.
Página 15 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...