Plane and Spherical Trigonometry, Surveying and Tables

Plane and Spherical Trigonometry, Surveying and Tables

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1895 edition. Excerpt: ...b cos C J "3. In the right triangle ABC, by 41, cos A = cos_p since--cossin (C--?/), or ( 28) cos A = cos sin C cos?/--cosp cos (7 sin y. Now, cossin?/--cos i?; 41 whence, cos Jp = cos B esc y, and coscos?/ = cos Bcoty = cos i? tan B cos z 43 = sin B cos a. Substituting these values of cos sin y and cos cos y in the value of cos A, we obtain cos A----cos B cos C + sin B sin C cos ai and similarly, cos B----cos A cos C + sin A sin C cos b 46 cosC =--cos A cos B + sin A sin B cose J Formulas 45 and 46 are also universally true; for the same equations are obtained when the arc CD cuts the side AB without the triangle. Exercise XXXIV. 1. What do Formulas 44 become if A = 90? if B = 90? if Or=90o? if a = 90? if A = B = 9Q? if a = 6 = 90o? 2. What does the first of 45 become if,4=0? if =90? if ==180? 3. Prom Formulas 45 deduce Formulas 46, by means of the relations between polar triangles ( 48). 54. Formulas For The Half Angles And Sides. From the first equation of 45, If we place A--B--C) = S, and proceed in the same manner as before, we obtain the following results: tanc = V--cosS cos (S--C) sec (S--A) sec (S--B) 55. Gauss's Equations And Napier's Analogies. By 27 5, cos-J-(A + B)--cos % A cos % B--sin J. sin-J-2?; or, by substituting for cos A, cos-J-i?, sin-J-t, sin-B, their values given in 54, and reducing, This value, by applying 29 12, 31 21, and observing that the expression under the radical is equal to sin J C, becomes, .. _ 2 sin-A-c cos ($-- -?)., _, cosb(A + B)=--0 2 1--v 1 2 ysm-(7: and this, by cancelling common factors, clearing of fractions, and observing that s--c = (a-f b), -reduces to the form cos (A + B) cos-J-c = cos (& + &) sin-C. more

Product details

  • Paperback | 58 pages
  • 189 x 246 x 3mm | 122g
  • United States
  • English
  • black & white illustrations
  • 1236790464
  • 9781236790460