 | August Ferdinand Möbius - 1886 - 717 pàgines
...(I), .. (IV) statt a i , b^, c t die Winkel A, B, C einführt, (I) sin b sin C = sin c sin B , (II) cos c — cos a cos b = sin a sin b cos C , (III) sin a cotg b = sin C cotg B + cos a cos C , (IV) cos C + cos A cos B = sin A sin B cos c .... | |
 | Webster Wells - 1887 - 200 pàgines
...(Art. 144) . tan rWhence, In like mauner we have, cos b = cos c cos a + sin c sin a cos B, (88) and cos c = cos a cos b + sin a sin b cos C. (89) 157. Let ABC and A'B'C' be a pair of polar triangles. Applying the theorem of Art. 156 to the... | |
 | G. Lion - 1891 - 170 pàgines
...b sin c cos A \ entre les trois (2) cos b = cos a cos c. -j- sin a sin c cos B > côtés et un (3) cos c = cos a cos b + sin a sin b cos C ) angle. sin a sin b sine ) entre deux côtés et les angles * sin A sinB sin C' l opposés. Si dans... | |
 | 1891 - 718 pàgines
...10. Resolve cos 6 into factors. Prove that 113 6 4?r c°S 5 11. Prove that in any spherical triangle cos c = cos a cos b + sin a sin b cos C, Prove that in any equilateral spherical triangle sec A = 1 + sec a. PUEE MATHEMATICS.— PART I. SECOND... | |
 | George Albert Wentworth - 1891 - 286 pàgines
...have an oblique spherical triangle with three sides given to find the angle C. Now from Formula [44], cos c = cos a cos b + sin a sin b cos C; then by substituting, cos d= cos (90°- 1) cos (90° - 1') + em(90°-Z) x sin (90°- 1') cos (m - m')... | |
 | Sir George Greenhill - 1892 - 386 pàgines
...vs ; so that o = am(/rt;1, l//c), 6 = am(xn;2, l//c), c = am(»c'U3, l//c). The fundamental formula cos c = cos a cos b + sin a sin b cos c now leads to the formula of § 121, dn va = dn i>jdn r, +/c2sn VjSn v2 en i>3, In the degenerate case... | |
 | Edward Albert Bowser - 1892 - 392 pàgines
...cos A + sin C sin A cos b. * From the nature of projections (Plane and Solid Geom., Art. 326). 13. cos C = — cos A cos B + sin A sin B cos c. 14. cot a sin b = cot A sin C + cos C cos b . . (Art. 193) 15. cot a sin с = cot A sin B + cos B cos... | |
 | Ferdinand Kraft, Hermann Grassmann - 1893 - 276 pàgines
...ergiebt sich aus (3) und sodann durch Buchstabenvertauschung cos b = cos c cos a — sin c sin a cos b,, cos c = cos a cos b — sin a sin b cos c,, cos a = cos b cos c — sin b sin c cos a,, welche Formeln den zweiten Fundamentalsatz der sphärischen... | |
 | Alexander Macfarlane - 1894 - 244 pàgines
...trigonometry is, c denoting the angle between the arcs A and B, and (7 denoting the opposite side. cos C = cos A cos B + sin A sin B cos c. A + B FIG. 1. Fio. 2. But suppose that the angle B of Fig. 1 is tilted up, and let c denote the angle... | |
 | 1894 - 448 pàgines
...C, these three points lie on a straight line, because the ordinary formula for a spherical triangle cos c= cos a cos b + sin a sin b cos C is easily transformed to cosa + b — cos a — b _ cos a + b — cose i— (— l) i— ( — cos... | |
| |
B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. 
