 | Isaac Todhunter - 1859 - 156 pàgines
...of great circles, shew that the angle BPC = twice the angle DPE, 13. Shew that sin b sin c + cos b cos c cos A = sin B sin C — cos B cos C cos a. 14. If Z) be any point in the side BC of a triangle, shew that cos AD sin BG = cos AB sin .0(7 + cos... | |
 | Isaac Todhunter - 1863 - 182 pàgines
...arcs of great circles, shew that the angle SPG= twice the angle DPE. 13. Shew that sin b sin c + cos b cos c cos A = sin B sin C ' — cos B cos C cos a. 14. If D be any point in the side BC of a triangle, shew that cos AD sin BC = cosAB sinDC + cosACsiuBD.... | |
 | Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 pàgines
...sines of the angles are proportional to the sines of the opposite sides, or by means of the equation cos a sin B sin C — cos B cos C = cos A. We may reduce the first member to a single term by placing cos a sin B = cos B cot $, i , . -o - ,n... | |
 | Dublin city, univ - 1871 - 366 pàgines
...the triangle. MR. LESLIE. 5. In a spherical triangle, prove geometrically that sin b sin c + cos b cos c cos A = sin B sin C — cos B cos C cos a ; deduce this relation also from the fundamental formulae. 6. Prove that the arc of a great circle... | |
 | Isaac Todhunter - 1879 - 176 pàgines
...angle BPO = twice the angle DPE. 13. In a spherical triangle shew that sin 6 sin с + cos b cos с cos A = sin B sin C — cos B cos C cos a. 14. If D be any point in the side BC of a triangle, shew that cos AD sin BC = cos AB sin DC + cos AC... | |
 | Dublin city, univ - 1878 - 498 pàgines
...whose rectangle is constant ? 4. In any spherical triangle, prove that sin j8 sin 7 + cos j3 cos y cos A = sin B sin C - cos B cos C cos a. 5. The roots of x3 4 fxi + qx + r = O are o, 0, y ; form an equation whose roots may be represented... | |
 | William Chauvenet - 1879 - 266 pàgines
...we have sin 6 sin c sin2 .4 = sin B sin (7 sin3 a, these two equations give, sin 6 sin c -f- cos 6 cos c cos A = sin B sin C — cos B cos C cos a (78) a relation between the six parts of the triangle, first given by CAGNOLI. It is a property of... | |
 | William John M'Clelland - 1885 - 182 pàgines
...we have « — »* a — a' ab tan — tan -j- = tan- — . 2. Prove that sin b sin e + cos b cos e cos A = sin B sin C — cos B cos C cos a. [If from the extremities of the base Л Л' quadrants A A' and .BB' be measured on the sides towards... | |
 | August Ferdinand Möbius - 1886 - 722 pàgines
...bei jedem der zwei Systeme 2 sin g sin h = 2 sin ^ (n -f- a — i) sin ^ (a + i — c) = cos (i — c) — cos a = sin b sin c + cos b cos c — cos a = sin 5 sin c (l — cos ^4) (§. 20, H) = 2 sin b sin c sin ^ .4* , und eben so ist sin h sin/ = sin... | |
 | Thomas Marcus Blakslee - 1888 - 56 pàgines
...ANGLES. Spherical. By law of cosines, cos A = • As in Plane, . cos a — cos b cos c siub sine 1 — cos A = '— : , , sin b sin c + cos b cos c — cos a sin b sm c = cosa-cos(6-c) (dif . of cos) — sin 6 sin c _ 2 sin(s — b) sin(s — c) sinb sine Similarly,... | |
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Shew that sin b sin c + cos b cos c cos A = sin B sin C 
