. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . >f the right triangle thus formed are denoted by letters, as in the figarc, we shall have these six formula: — 1. sin, A = 2. COS. A = - . 3. tan. A = 4. cosec. -^-l 5. sec. ■^-l 6. cot. a Given-a. c a, b J., a A,b 10 11 :.4. c Solution ofRijht Triangles (fig. 57).,B,l A, B, cB,b,c B,
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . >f the right triangle thus formed are denoted by letters, as in the figarc, we shall have these six formula: — 1. sin, A = 2. COS. A = - . 3. tan. A = 4. cosec. -^-l 5. sec. ■^-l 6. cot. a Given-a. c a, b J., a A,b 10 11 :.4. c Solution ofRijht Triangles (fig. 57).,B,l A, B, cB,b,c B, a, cB,a,b Formulae. a sin.^=-, cos. C = -, b=-^ic-\-a){c — a) c c tan. A = :^ , cot. B = -^ , c = ya* -f b*. B =.90° — A, b = a cot. A, c =^B = 90o — A. a = c = sin. Ab COS. A B=--90° — A. a = , i = c cos. .4 134 TABLE X. TRIGONOMETRICAL AND Solution of Oblique Triangles (fig. 58). Fig. 58. 121314 15 1617 18 , B, a A, a, b a,b, C a, 6, c A,B,C,aA, b, c a, b, c Sought. Ib B b = sin. B a sin. Bsin. A b sin. Aa Formulae. A — Btan.^ {A — B) ja — b) can, i (A + B) •Ifs=i(a + 6 + c), sm. ^A=^l^^l^.cos4^= J^\ ^= J(f^i^>, •^ y/ be ^ > 5(5 —O) . sin. A = 2 .^A* (5 — a){s — b) (s — c) be a- sin. B sit C areaareaarea area = 2 sin. Aarea = hbc sin. A. s=i (a 4- 6 + r,, area=ys {s—a) {s—b) {«- «). General Trigoriometri<v* Fomnilce. 19!20212223242526272829•30!3I sin. J. + cos.^ yl = 1. .= 9 sin. (J. ± B) = .sin. ^1 cos. 75 ± sir h cos. {A da B) = COS. ^ COS. B rp sin. .^ in. 2 A = 2 sin. ^ cos. ^.COS. 2 J. = A — sin,2 J^ == i _ o siii i sin. A = h — k ^os- 2 ^• ^ ^ i + ^ COS. 2 ^. sin. J. + sin. B = 2 sin. ^ (^ + S) cos. ^ (^ ZJ).sin. .-1 — sin. B = 2 cos. ^ (^ + 5) sin.^ [A B).COS. ^ + cos. B =-2 cos. |(A + JB) cos. ^ (J. • fJ).cos. B — cos. ^ = 2 sin. ^ [A-\-B) sin. ^ (^ — P) A —
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
