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Plane Trigonometry for the Use of Colleges and Schools; With Numerous Examples

Plane Trigonometry for the Use of Colleges and Schools; With Numerous Examples


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1860 Excerpt: ...--J approximately, = (cos 0)4 approximately, therefore log sin 0 = log 0 + J log cos 0 approximately. This formula gives log sin 0 at once if 6 be given. If log sin 0 be given, we must find an approximate value of 0, and then find log cos 0 approximately; then we have log 0 = log sin 0--log cos 0. Here since cos 6 varies far less rapidly than 0, we are free from sensible error by using an approximate value of log cos 0 instead of the real value. A similar formula may be found for the tangent of a small angle; for ten 6 = coll = 6 j) ( J) aPProximately tWo !-._(!_;)(!. J) = 1 + = 1--approximately, therefore log tan 0 = log 0--f log cos 0 approximately. 206. We will now sum up the results of the investigations of the present chapter. The principle of proportional parts is applicable to all the trigonometrical functions natural and logarithmic with certain exceptions, which occur when the angles are small or nearly equal to a right angle. In the exceptional cases the differences of consecutive functions are sometimes irregular only; sometimes they are nearly insensible, and then they are also irregular. For the natural functions we have the following exceptional cases. For the sine the differences are insensible when the angles are nearly right angles; for the cosine they are insensible when the angles are small. For the tangent the differences are irregular when the angles are nearly right angles; for the cotangent they are irregular when the angles are small. For the secant the differences are insensible when the angles are small, and irregular when they are nearly right angles; for the cosecant the differences are irregular when the angles are small, and insensible when they are nearly right angles. For every logarithmic function the principle of prop...


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Product Details
  • ISBN-13: 9781130480078
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 50
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130480070
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 109 gr

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