PLANE TRIGONOMETRY WITH TABLES

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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 function 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
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Functions of ir + 9 in terms of functions of 9
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Functions of x + 9 in terms of functions of 9
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Summary of the reduction formulas
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Proof of the reduction formulas for any value of 9
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Values for all angles that have a given sine or cosecant
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Values for all angles having the same cosine or secant
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Values for all angles that have the same tangent or cotangent
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Changes in the value of the sine and cosine as the angle increases from 0 to 360
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Graph of y sin 9
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Mechanical construction of graph of sin 9
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Inverse functions
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Graph of y sin1 x or y arc sin x
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Relation between sin 9 9 and tan 9
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FUNCTIONS OF SUMS AND DIFFERENCES OF ANGLES Art Page 65 Addition and subtraction formulas
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Derivation of the formulas for sine and cosine of the difference of two angles
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Proof of the addition formulas for other values of the angles
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Proof of the subtraction formulas for other values of the angles
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Case III The solution of a triangle when two sides and the included angle are given First method
109
Case III Second method
110
Case III Third method
112
Case IV The solution of a triangle when the three sides are given
113
Case IV Formulas adapted to the use of logarithms
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CHAPTER VII
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To solve r sin 6 + s cos d t for 6 when r s and t are known
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Equations in the form sin a + 0 c sin a where 3 and c are known
130
Equations in the form tan a + 0 c tan a where ft and c are known
131
Computation of trigonometric functions
145
Art Page 1 Use of logarithms 1
1
Definitions 2
2
Systems of logarithms 3
3
Logarithms to the base 10 4
4
Rules for determining the characteristic 6
6
The mantissa 7
7
To find the mantissa of the logarithm of a number 8
8
Rules for finding the mantissa 9
9
Finding the logarithm of a number 10
10
Rules for finding the number corresponding to a logarithm 12
12
To multiply by means of logarithms 13
13
Cologarithms 14
14
To find the root of a number by means of logarithms 15
15
Proportional parts 16
16
Changing systems of logarithms 19
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Use of Table II 20
20
To find logarithmic function of an acute angle 22
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To find the acute angle corresponding to a logarithmic function 23
23
Angles near 0 and 90 24
24
Functions by means of S and T 25
25
Functions of angles greater than 90 26
26
Table IV Explanatory 27
27
Table V Explanatory 28
28
Logarithms of Numbers 31
31
Conversion of Logarithms 52
52
Logarithms of Trigonometric Functions 53
53
Natural Trigonometric Functions 107
107
Radian Measure 131
131
Constants and Their Logarithms 132
132
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Pàgina 2 - 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.
Pàgina 139 - The cube root of a number is one of the three equal factors of the number. Thus the cube...
Pàgina 101 - CASE II. Given two sides and an angle opposite one of them. CASE III.
Pàgina 13 - 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.
Pàgina 101 - In any triangle the sides are proportional to the sines of the opposite angles.
Pàgina ii - Electrical World The Engineering andMining Journal Engineering Record Engineering News Railway Age Gazette American Machinist Signal Engineer American Engineer Electric Railway Journal Coal Age Metallurgical and Chemical Engineering Power ANALYSIS BY EDWARD G.
Pàgina 4 - 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.
Pàgina 110 - 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.
Pàgina 14 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.
Pàgina 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

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