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58
9
10, 11
1114
15, 16
1018. Relations of the six functions to one another.
TABLE I. Natural values of the functions to three
places for each degree of the quadrant
27, 28.
Given the hypothenuse and an acute angle.
Formulas [16] and [17]
29, 30. Given one leg and the angle opposite.
Formulas [18] and [19] .
31, 32. Given one leg and the acute angle adjacent.
PAGE
17
17, 18
18, 19
19
19, 20
ARTICLE
35, 36. Given the two legs. Formulas [24][26] .

37. Exercises, including various applications, — isosceles
triangles (p. 26), regular polygons (p. 27).
3853. Logarithmic solution of right triangles.
Formulas [27][38]
54. Exercises.
CHAPTER III.
20
2128
2933
34
THE SOLUTION OF OBLIQUE TRIANGLES BY DRAWING A
PERPENDICULAR.
55, 56. Preliminary
5762. Given one side and two angles
63. Exercises
6468. Given two sides and the included angle
69. Exercises
7076. Given two sides and the angle opposite one of them
77. Exercises
35
3537
38
3941
41, 42
4351
52, 53
95, 96. Positive and negative lines. Formulas [42][44].
99, 100. Positive and negative values of the functions
101107. Limiting values of the functions
73, 74
74, 75
7577
108116. Variation of the functions between their limiting
values.
TABLE II. Functions of Angles in all Quadrants
117–123. Formulas [3][14] generalized and repeated in
Formulas [46][52] with illustrations
.
7779
80
8184
123. Each function expressed in terms of each of the
others
84, 85
124129. The functions represented by lines drawn in con
nection with a unitcircle
8589
Formula [54]
Formula [55]
Formula [56]
130. The functions of a negative angle. Formula [53]
131. The functions of A+ 90°.
132. The functions of A + 180°.
133. The functions of A + 270°.
134. The functions of A±k 360°.
135, 136. The functions of any angle whatever. Examples
illustrating the use of Formulas [53][57]
Formula [57]
137. The logarithmic functions of any angles whatever
138. Exercises
90, 91
92, 93
94, 95
95
95, 96
9699
99, 100
101
CHAPTER V.
PROJECTIONS.
139–145. Projections defined. Positive and negative projec
tions. Projecting angle. The projection of a
broken line; of the perimeter of a polygon; of the perimeter of a triangle. Formulas [58][60] . 102106
CHAPTER VI.
GENERAL FORMULAS.
146. The sine and the cosine of the sum of two angles.
149, 150. The sine and the cosine of the difference of two
112114
angles. Formulas [63] and [64] .
151. Formulas for the sine and cosine of the difference
of two angles deduced from those for the sine
and cosine of the sum
114, 115
152. The tangent and the cotangent of the sum, and of
the difference of two angles. Formulas [65][68] 115, 116
153. Functions of the double and of the half of an angle.
Formulas [69][91] .
116118
154, 155. Sums and differences of functions.
Formulas [92][101]
118120
156168. Particular results deduced from the general formu
las
120124
169. Formulas [102]–[113], giving the sine and the cosine
of the sum and of the difference of two angles,
one of the angles being 90°, 180°, 270°, or 360°
CHAPTER VII.
PLANE TRIANGLES.
125
171, 172. Each side of a triangle equal to the algebraic sum
of the projections upon it of the other two sides.
Formula [114]
173. The cyclic relation of formulas relating to triangles
174. The analytic and synthetic methods
175, 176. The sides of a plane triangle proportional to the
sines of the opposite angles. Analytic proof.
The modulus. Geometric proof.
Formulas [115] and [116]
177, 178. The sines of the angles of a triangle equal to the
ratios of the opposite sides to the diameter of
the circumscribed circle. This diameter equal to
the modulus. Formula [117]
126, 127
127
128
128130
131, 132
179181. The sum of two sides of a triangle to their differ
ence as the tangent of half the sum of the oppo
site angles to the tangent of half their difference.
Analytic proof. Geometric proof. Ratio of the
sum and of the difference of two sides to the
third side. Formulas [118], [119 a], and [119 b] . 132135
182, 183. The square of one side of a triangle equal to the
sum of the squares of the other two sides less
twice their product multiplied by the cosine of
the angle included by them. Analytic proof.
Geometric proof. Formula [120] .
135138