Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 13
... proved by repeated use of Art . 29. Suppose , for example , the figure has four sides , and let the angular points be denoted by A , B , C , D. Then therefore , ABBC is greater than AC ; AB + BC + CD is greater than AC + CD , and à ...
... proved by repeated use of Art . 29. Suppose , for example , the figure has four sides , and let the angular points be denoted by A , B , C , D. Then therefore , ABBC is greater than AC ; AB + BC + CD is greater than AC + CD , and à ...
Página 17
... proved , cos a = cos b cos c ' + sin b sin c ' cos B'AC " ; but a = π- -α , π - с , BAC = π - A ; thus cos a = cos b cos c + sin b sin c cos A. ( 2 ) Suppose both the sides which contain the angle A to be greater than quadrants ...
... proved , cos a = cos b cos c ' + sin b sin c ' cos B'AC " ; but a = π- -α , π - с , BAC = π - A ; thus cos a = cos b cos c + sin b sin c cos A. ( 2 ) Suppose both the sides which contain the angle A to be greater than quadrants ...
Página 18
... proved to be universally true . 39. The formula in Art . 37 may be applied to express the cosine of any angle of a triangle in terms of sines and cosines of the sides ; thus we have the three formulæ , cos a = cos_b_cos c + sin b sin c ...
... proved to be universally true . 39. The formula in Art . 37 may be applied to express the cosine of any angle of a triangle in terms of sines and cosines of the sides ; thus we have the three formulæ , cos a = cos_b_cos c + sin b sin c ...
Página 20
... prove that cot a sin b = cot A sin C + cos b cos C. We have cos a = cos b cos c + sin b sin c cos A , cos c = cos a cos b + sin a sin b cos C , sin C sin c = sin a sin A thus Substitute the values of cos c and sine in 20 RELATIONS ...
... prove that cot a sin b = cot A sin C + cos b cos C. We have cos a = cos b cos c + sin b sin c cos A , cos c = cos a cos b + sin a sin b cos C , sin C sin c = sin a sin A thus Substitute the values of cos c and sine in 20 RELATIONS ...
Página 24
... S cos ( S - 4 ) cos ( S - B ) cos ( S — C ' ) } . We shall use N for { - cos S cos ( S - A ) cos ( S - B ) cos ( S — C ' ) } 3 . -- a 2 52. To prove Napier's Analogies . We have sin A 24 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... S cos ( S - 4 ) cos ( S - B ) cos ( S — C ' ) } . We shall use N for { - cos S cos ( S - A ) cos ( S - B ) cos ( S — C ' ) } 3 . -- a 2 52. To prove Napier's Analogies . We have sin A 24 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Otras ediciones - Ver todas
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1949 |
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1929 |
Términos y frases comunes
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
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