Spherical Trigonometry ... |
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Page 18
... formulæ , cos a = 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 ...
... formulæ , cos a = 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 ...
Page 19
... formulæ from them . 40. To express the sine of an angle of a spherical triangle . We have cos A = cos a cos b cos c - sin b sin c therefore sin2 A = 1 - ( therefore sin A = ; COS a cos b cos - sin b sin c - 2 ( 1 − cos3 b ) ( 1 − cos3 ...
... formulæ from them . 40. To express the sine of an angle of a spherical triangle . We have cos A = cos a cos b cos c - sin b sin c therefore sin2 A = 1 - ( therefore sin A = ; COS a cos b cos - sin b sin c - 2 ( 1 − cos3 b ) ( 1 − cos3 ...
Page 21
... formulæ may be obtained like that in the preceding article ; the whole six formulæ will be as follows : cot a sin b = cot A sin C + cos b cos C , cot b sin a = cot B sin C + cos a cos C , cot b sin c cot B sin A + cos c cos A , - cot c ...
... formulæ may be obtained like that in the preceding article ; the whole six formulæ will be as follows : cot a sin b = cot A sin C + cos b cos C , cot b sin a = cot B sin C + cos a cos C , cot b sin c cot B sin A + cos c cos A , - cot c ...
Page 23
... formulæ over again . This consideration will furnish some assist- ance in retaining those formulæ accurately in the memory . 49. To express the sine , cosine , and tangent , of half a side of a triangle as functions of the angles . We ...
... formulæ over again . This consideration will furnish some assist- ance in retaining those formulæ accurately in the memory . 49. To express the sine , cosine , and tangent , of half a side of a triangle as functions of the angles . We ...
Page 26
... formulæ in Art . 39 . 53. In equation ( 4 ) of the preceding article , cos ( a - b ) and C cot are necessarily positive quantities ; hence the equation shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus & ( A + B ) ...
... formulæ in Art . 39 . 53. In equation ( 4 ) of the preceding article , cos ( a - b ) and C cot are necessarily positive quantities ; hence the equation shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus & ( A + B ) ...
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Common terms and phrases
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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