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

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

Contents

Table giving Changes of Functions in Four Quadrants
28
Relations between the Functions of the Same Angle
29
Use of the Preceding FormulŠ
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
FormulŠ for transforming Sums into Products
55
Useful FormulŠ
56
Tangent of Sum and Difference of Two Angles
57
FormulŠ 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 FormulŠ
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

Other editions - View all

Common terms and phrases

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