Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 σελίδες |
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Σελίδα 19
... 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 b cos therefore sin2 A = 1 – sin b sin c c ) 2 - - ( 1 ...
... 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 b cos therefore sin2 A = 1 – sin b sin c c ) 2 - - ( 1 ...
Σελίδα 22
... deduce A tan = sin s sin ( s - a ) ́sin ( s — b ) sin ( s – c ) ) The positive sign must be given to the radicals which occur in A 2 this article , because is less than a right angle , and therefore its sine , cosine , and tangent are ...
... deduce A tan = sin s sin ( s - a ) ́sin ( s — b ) sin ( s – c ) ) The positive sign must be given to the radicals which occur in A 2 this article , because is less than a right angle , and therefore its sine , cosine , and tangent are ...
Σελίδα 27
... deduced analytically from those in Art . 39 , and thus the whole subject may be made to depend upon the formulæ of Art ... deduce the following theorem : If the sides and angles of a spherical triangle be changed respectively into the ...
... deduced analytically from those in Art . 39 , and thus the whole subject may be made to depend upon the formulæ of Art ... deduce the following theorem : If the sides and angles of a spherical triangle be changed respectively into the ...
Σελίδα 31
... deduce the limits between which the sides and angles of an equilateral triangle are restricted . 8. In an equilateral triangle , shew that sec A 1 + sec a . = 9. If the three sides of a spherical triangle be halved and a new triangle ...
... deduce the limits between which the sides and angles of an equilateral triangle are restricted . 8. In an equilateral triangle , shew that sec A 1 + sec a . = 9. If the three sides of a spherical triangle be halved and a new triangle ...
Σελίδα 58
... deduced from that of Art . 86 . EXAMPLES . 1. The sides of a triangle are 105 ° , 90 ° , and 75 ° respectively ; find the sines of all the angles . 2 . Shew that tan A tan B Sin ( 8 - c ) Solve a triangle = sin s when a side , an ...
... deduced from that of Art . 86 . EXAMPLES . 1. The sides of a triangle are 105 ° , 90 ° , and 75 ° respectively ; find the sines of all the angles . 2 . Shew that tan A tan B Sin ( 8 - c ) Solve a triangle = sin s when a side , an ...
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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
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