A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous Examples

Edward Albert Bowser

D.C. Heath & Company, 1892 - Trigonometry - 368 pages

Contents

• PART: 1
• ᎪᎡᎢ PAGE 179 Sum the Series tan + tan + tan + etc 255: 3
• Comparison of the Sexagesimal and Centesimal Measures: 8
• CHAPTER II: 16
• Representation of the Functions by Straight Lines: 23
• Changes in Sine as the Angle increases from 0 to 360: 25
• Changes in Cosine as the Angle increases from 0 to 360: 26
• Changes in Tangent as the Angle increases from 0 to 360: 27
• Table giving Changes of Functions in Four Quadrants: 28
• Relations between the Functions of the Same Angle: 29
• Use of the Preceding Formulæ: 30
• To find the Trigonometric Functions of 45: 31
• To find the Trigonometric Functions of 60 and 30: 33
• Functions of Complemental Angles: 34
• To prove sin 90 + A cos A etc: 35
• To prove sin A sin A etc: 36
• Table giving the Reduced Functions of Any Angle: 37
• Periodicity of the Trigonometric Functions: 38
• Angles corresponding to Given Functions: 39
• General Expression for All Angles with a Given Sine: 40
• An Expression for All Angles with a Given Cosine: 41
• Trigonometric Identities: 43
• Examples: 44
• CHAPTER III: 50
• To find the Values of sin x y and cos x y: 52
• Quadruple Values of Sine and Cosine of Half an Angle: 54
• Formulæ for transforming Sums into Products: 55
• Useful Formulæ: 56
• Tangent of Sum and Difference of Two Angles: 57
• Formulæ for the Sum of Three or More Angles: 58
• Functions of Double Angles: 60
• Functions of 3 x in Terms of the Functions of x: 61
• Functions of Half an Angle: 63
• Find the Values of the Functions of 2210: 69
• Table of Useful Formulæ: 75
• CHAPTER IV: 87
• Comparison of Two Systems of Logarithms: 93
• To find the Angle whose Sine is Given: 108
• To find the Angle whose Logarithmic Cosine is Given: 115
• To solve r cos o cos 0 a rcos sin: 138
• CHAPTER VI: 146
• To express the Sine of an Angle in Terms of the Sides: 152
• CHAPTER VII: 165
• Case I: 167
• Case III Given Two Sides and the Included Angle: 176
• Heights of an Accessible Object: 182
• Problem of Pothenot or of Snellius: 188
• ᎪᎡᎢ: 201
• CHAPTER VIII: 204
• Quadrantal and Isosceles Triangles: 207
• To calculate the Sine and Cosine of 10 and of: 211
• Tables of Logarithmic Trigonometric Functions: 217
• To prove the Rule for the Table of Common Logarithms: 218
• To prove the Rule for the Table of Natural Sines 146 To prove the Rule for a Table of Natural Cosines: 219
• To prove the Rule for a Table of Natural Tangents: 220
• To prove the Rule for a Table of Logarithmic Sines 149 To prove the Rule for a Table of Logarithmic Cosines 150 To prove the Rule for a Table of ...: 221
• Case II: 222
• Cases of Inapplicability of Rule of Proportional Parts 152 Three Methods to replace the Rule of Proportional Parts: 224
• Examples: 226
• CHAPTER IX: 229
• and cos 0: 233
• To develop sin and cos in Series of Powers of 0: 234
• Convergence of the Series 158 Expansion of cos: 235
• Expansion of sin in Terms of Cosines of Multiples of 0: 236
• Expansion of sin 0 in Terms of Sines of Multiples of 161 Exponential Values of Sine and Cosine: 238
• Gregorys Series: 239
• Eulers Series: 240
• Machins Series 165 Given sin x sin 0+ a expand 229 Р 231 233 234 235 235 236 237 238 239 240: 241
• in Powers of x: 242
• 248: 248
• 252: 252
• Given tan x n tane expand x in Powers of n 167 Resolve: 254
• Sum the Series sin a + x sin α+ B + etc: 255
• Summation of Infinite Series: 256
• Examples: 257
• PART II: 267
• Fundamental Definitions and Properties: 268
• Formulæ for Right Spherical Triangles: 270
• Napiers Rules: 272
• The Species of the Parts: 273
• Ambiguous Solution: 274
• Law of Sines: 276
• Law of Cosines: 277
• Relation between a Side and the Three Angles: 278
• To find the Value of cot a sin b etc: 279
• Useful Formulæ: 280
• Formulæ for the Half Angles: 281
• Formulæ for the Half Sides: 284
• Napiers Analogies: 286
• Delambres or Gausss Analogies: 287
• Examples: 288
• CHAPTER XI: 297
• CHAPTER XII: 324
• Areas of Triangles Given the Three Sides: 331
• CHAPTER XIII: 338
• The Chordal Triangle: 346
• Reduction of an Angle to the Horizon: 352
• ᎪᎡᎢ PAGE: 353
• Table of Formulæ in Spherical Trigonometry: 359

Popular passages

Page 148 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.

Page 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.

Page 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.

Page 278 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...

Page 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...

Page 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 149 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Bibliographic information

• Title: A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous Examples
• Author: Edward Albert Bowser
• Contributor: D.C. Heath and Company
• Publisher: D.C. Heath & Company, 1892
• Original from: the University of California
• Digitized: Nov 29, 2007
• Length: 368 pages