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Practical Mathematics; Being the Essentials of Arithmetic, Geometry, Algebra and Trigonometry Volume 4

Practical Mathematics; Being the Essentials of Arithmetic, Geometry, Algebra and Trigonometry Volume 4


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About the Book

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. 1913 edition. Excerpt: ...this way. It includes the angles for every 10' from 0 to 90. 34. Use of functions in constructing angles. Example 1.--Construct an angle of 40. Construction.--Sin 40 =0.64. By the help of this, the angle may be drawn as follows: Draw a straight line AB, Fig. 13. At some point Q, erect a perpendicu lar QP 0.64 in. in length. With P as a center draw an arc with a radius of 1 in. cutting AB at O. Draw OP. Angle QOP is 40, for sin QOP =0.64 = sin 40. In constructing an angle of 40, all that is necessary is to make the sides QP and OP of such lengths that the ratio shall be 0.64. For this 1.28 in. and 2 in. could be used conveniently. Usually it is most convenient to make one of the sides unity. In making the construction, some other function of 40 could be used as well as the sine. Example 2.--Construct an angle of 35 by using tan 35. Construction.--tan 35 =0.70. Draw a straight line MN, Fig. 14. At some point Q erect a perpendicular QP to MN 0.70 in. in length. Locate O making OQ =1 in. Draw OP. Angle QOP is 35, for tan QOP = 0.70 = tan 35. 1. Construct by the use of sines angles of 25, 65, 47, 53 20', and 25 30'. Suggestion.--Use data from the table of Art. 33 or from Table II. 2. Construct by use of cosines angles of 20, 40, 17 20', and 67 40'. 3. Construct an angle 0 whose tangent is 2. Find the other functions of this angle. Ans. sin 0 =.89; cos 0=.45; cot 0 =.5O; sec 0 = 2.24; esc 6 = 1.12. 35. Values of functions by computation.--From our knowledge of geometry, we know the relations between the sides and the angles of right triangles when the acute angles are 30, 45, or 60. Thus, when the acute angles are 45 each, the two legs are equal; and if they are given the hypotenuse can be found. If one acute angle is 30 and the other 60, the...


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Product Details
  • ISBN-13: 9781234374433
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1234374439
  • Publisher Date: 22 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 64 gr


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