Plane and Spherical Trigonometry

Front Cover
McGraw-Hill Book Company, 1916 - Logarithms - 188 pages

From inside the book

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

To each and every angle there corresponds but one value of each trigonometric ratio
14
Signs of the trigonometric functions
15
Trigonometric functions by computation
16
Given the function of an angle to construct the angle
20
Trigonometric functions applied to right triangles
22
Relations between the functions of complementary angles
23
Given the function of an angle in any quadrant to construct the angle
24
Fundamental relations between the functions of an angle
27
To express one funotion in terms of each of the other functions
29
Transformation of trigonometric expressions so as to contain but one function
31
Identities
32
Inverse trigonometric functions
34
ART PAGE 28 General statement
37
The solution of right triangles by computation
38
Steps in the solution
39
Solution of right triangles by natural functions
40
Remark on logarithms
43
Definitions
45
Accuracy
51
Tests of accuracy
52
Orthogonal projection
53
Distance and dip of the horizon
56
CHAPTER IV
61
Functions of to in terms of functions of 0
63
Functions of r + Q in terms of functions of 0
64
Functions of fr to in terms of functions of o
65
Summary of the reduction formulas
66
Proof of the reduction formulas for any value of 0
68
Values for all angles that have a given sine or cosecant
69
Values for all angles having the same cosine or secant
70
Values for all angles that have the same tangent or cotangent
71
Changes in the value of the sine and cosine as the angle increases from 0 to 360
74
Graph of y sin 0
75
Mechanical construction of graph of sin 8
76
Inverse functions
77
Graph of y sin + x or y arc sin 2
78
Relation between sin 0 0 and tan 0
79
FUNCTIONS OF SUMS AND DIFFERENCES OF ANGLES ART PAGE 65 Addition and subtraction formulas
83
Derivation of the formulas for sine and cosine of the difference of two angles
84
Proof of the addition formulas for other values of the angles
85
Proof of the subtraction formulas for other values of the angles
86
Formulas for the tangents of the sum and the difference of two angles
89
Functions of an angle in terms of functions of half the angle
90
Functions of an angle in terms of functions of twice the angle
92
Case IV The solution of a triangle when the three sides are given
113
Case IV Formulas adapted to the use of logarithms
114
CHAPTER VII
127
To solve r sin 0 + 8 cos 0 t for 0 when r s and t are known
129
Equations in the form sina + B c sin a where B and c are known
130
Equations in the form tana + B c tan a where B and c are known
131
CHAPTER VIII
134
Complex number in terms of amplitude and modulus
135
Multiplication of complex numbers
136
Division of two complex numbers
138
Cube roots of a number
139
To find the nth roots of a number
141
Expansion of sin n8 and cos no
143
Computation of trigonometric functions
145
Series for sin and cos in terms of sines or cosines of multiples of 0
146
Hyperbolic functions
148
Relations between the hyperbolic functions
149
Relations between the trigonometric and the hyperbolic functions
150
CHAPTER IX
151
Angles and sides of spherical triangles
152
Right spherical triangle
153
Derivation of formulas for right spherical triangles
154
Napiers rules of circular parts
155
Species
156
Solution of right spherical triangles
157
Isosceles spherical triangles
159
Sine theorem Law of sines
160
Cosine theorem Law of cosines
161
Theorem
162
Given the three sides to find the angles
163
Given the three angles to find the sides
164
Napiers analogies
165
Gausss equations
167
Rules for species in oblique spherical triangles
168
Cases
169
Case I Given the three sides to find the three angles
170
Case II Given the three angles to find the three sides
171
Area of a spherical triangle
175
A
1
B
8
E
16
M
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page 4 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 141 - The cube root of a number is one of the three equal factors of the number. Thus the cube...
Page 15 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 103 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 8 - When the number is greater than 1, the characteristic is positive, and is one less than the number of digits to the left of the decimal point...
Page 17 - To find any power of a given number, multiply the logarithm of the number by the exponent of the power. The product is the logarithm of the power.
Page 112 - 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.
Page 6 - In it the right angle is divided into 100 equal parts called grades, the grade into 100 equal parts called minutes, and the minute into 100 equal parts called seconds.
Page 163 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Page 16 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.

Bibliographic information