Plane And Spherical Trigonometry Fourth Edition Thirteenth Impression2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Plane And Spherical Trigonometry Fourth Edition Thirteenth ImpressionPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER Ⅰ INTRODUCTION1

1．Introductory remarks1

2．Angles，definitions2

3．Quadrants3

4．Graphical addition and subtraction of angles3

5．Angle measurement4

6．The radian5

7．Relations between radian and degree6

8．Relations between angle，arc，and radius8

9．Area of circular sector10

10．General angles12

11．Directed lines and segments13

12．Rectangular coordinates14

13．Polar coordinates15

CHAPTER Ⅱ TRIGONOMETRIC FUNCTIONS OF ONE ANGLE17

14．Functions of an angle17

15．Trigonometric ratios17

16．Correspondence between angles and trigonometric ratios18

17．Signs of the trigonometric functions19

18．Calculation from measurements20

19．Calculations from geometric relations21

20．Trigonometric functions of 30°21

21．Trigonometric functions of 45°22

22．Trigonometric functions of 120°22

23．Trigonometric functions of 0°23

24．Trigonometric functions of 90°23

25．Exponents of trigonometric functions25

26．Given the function of an angle，to construct the angle26

27．Trigonometric functions applied to right triangles28

28．Relations between the functions of complementary angles30

29．Given the function of an angle in any quadrant，to construct the angle31

CHAPTER Ⅲ RELATIONS BETWEEN TRIGONOMETRIC FUNCTIONS34

30．Fundamental relations between the functions of an angle34

31．To express one function in terms of each of the other functions36

32．To express all the functions of an angle in terms of one function of the angle，by means of a triangle37

33．Transformation of trigonometric expressions38

34．Identities40

35．Inverse trigonometric functions42

36．Trigonometric equations43

CHAPTER Ⅳ RIGHT TRIANGLES47

37．General statement47

38．Solution of a triangle47

39．The graphical solution48

40．The solution of right triangles by computation48

41．Steps in the solution49

42．Remark on logarithms54

43．Solution of right triangles by logarithmic functions54

44．Definitions56

CHAPTER Ⅴ FUNCTIONS OF LARGE ANGLES62

46．Functions of 1/2π－θ in terms of functions of θ62

47．Functions of 1/2π＋θ in terms of functions of θ63

48．Functions of π－θ in terms of functions of θ63

49．Functions of π＋θ in terms of functions of θ64

50．Functions of 3/2π－θ in terms of functions of θ65

51．Functions of 3/2π＋θ in terms of functions of θ65

52．Functions of-θ or 2π-θ in terms of functions of θ66

53．Functions of an angle greater than 2π67

54．Summary of the reduction formulas67

55．Solution of trigonometric equations71

CHAPTER Ⅵ GRAPHICAL REPRESENTATION OF TRIGONOMETRIC FUNCTIONS76

56．Line representation of the trigonometric functions76

57．Changes in the value of the sine and cosine as the angle increases from 0 to 360°78

58．Graph of y=sin θ79

59．Periodic functions and periodic curves80

60．Mechanical construction of graph of sin θ82

61．Projection of point having uniform circular motion83

62．Summary85

63．Simple harmonic motion86

64．Inverse functions87

65．Graph of y=sin-1 x，or y=arc sin x87

CHAPTER Ⅶ PRACTICAL APPLICATIONS AND RELATED PROBLEMS90

66．Accuracy90

67．Tests of accuracy91

68．Orthogonal projection92

69．Vectors93

70．Distance and dip of the horizon95

71．Areas of sector and segment99

72．Widening of pavements on curves97

73．Reflection of a ray of light102

74．Refraction of a ray of light102

75．Relation between sin θ，θ，and tan θ，for small angles103

76．Side opposite small angle given105

77．Lengths of long sides given105

CHAPTER Ⅷ FUNCTIONS INVOLVING MORE THAN ONE ANGLE108

78．Addition and subtraction formulas108

79．Derivation of formulas for sine and cosine of the sum of two angles108

80．Derivation of the formulas for sine and cosine of the difference of two angles109

81．Proof of the addition formulas for other values of the angles110

82．Proof of the subtraction formulas for other values of the angles110

83．Formulas for the tangents of the sum and the difference of two angles113

84．Functions of an angle in terms of functions of half the angle114

85．Functions of an angle in terms of functions of twice the angle117

86．Sum and difference of two like trigonometric functions as a product119

87．To change the product of functions of angles to a sum122

88．Important trigonometric series123

CHAPTER Ⅸ OBLIQUE TRIANGLES130

89．General statement130

90．Law of sines130

91．Law of cosines132

92．Case Ⅰ．The solution of a triangle when one side and two angles are given132

93．Case Ⅱ．The solution of a triangle when two sides and an angle opposite one of them are given136

94．Case Ⅲ．The solution of a triangle when two sides and the included angle are given First method140

95．Case Ⅲ．Second method140

96．Case Ⅳ．The solution of a triangle when the three sides are given143

97．Case Ⅳ．Formulas adapted to the use of logarithms144

CHAPTER Ⅹ MISCELLANEOUS TRIGONOMETRIC EQUATIONS158

98．Types of equations158

99．To solve r sin θ + s cos θ = t for θ when r， s， and t are known160

100．Equations in the form p sin α cos β = a， p sin α sin β3 = b， p cos α =c， where p，α，and β are variables161

101．Equations in the form sin （α + β） = c sin α， where β and c areknown161

102．Equationsin the form tan （α + β） = c tan α， where β3 and c areknown162

103．Equations of the form t = θ + φ sin t， where θ and φ are givenangles162

CHAPTER Ⅺ COMPLEX NUMBERS， DEMOIVRE＇S THEOREM， SERIES165

104．Imaginary numbers165

105．Square root of a negative number165

106．Operations with imaginary numbers166

107．Complex numbers166

108．Conjugate complex numbers167

109．Graphical representation of complex numbers167

110．Powers of i169

111．Operations on complex numbers169

112．Properties of complex numbers171

113．Complex numbers and vectors171

114．Polar form of complex numbers172

115．Graphical representation of addition174

116．Graphical representation of subtraction175

117．Multiplication of complex numbers in polar form176

118．Graphical representation of multiplication176

119．Division of complex numbers in polar form176

120．Graphical representation of division177

121．Involution of complex numbers177

122．DeMoivre＇s theorem for negative and fractional exponents178

123．Evolution of complex numbers179

124．Expansion of sin nθ and cos nθ182

125．Computation of trigonometric functions184

126．Exponential values of sin θ， cos θ， and tan θ184

127．Series for sinn θ and cosn θ in terms of sines or cosines of multiples of θ185

128．Hyperbolic functions187

129．Relations between the hyperbolic functions188

130．Relations between the trigonometric and the hyperbolic functions188

131．Expression for sinh x and cosh x in a series．Computation189

131．Forces and velocities represented as complex numbers189

CHAPTER Ⅻ SPHERICAL TRIGONOMETRY193

132．Great circle， small circle， axis193

133．Spherical triangle193

134．Polar triangles194

135．Right spherical triangle195

136．Derivation of formulas for right spherical triangles196

137．Napier＇s rules of circular parts197

138．Species198

139．Solution of right spherical triangles198

140．Isosceles spherical triangles200

141．Quadrantal triangles201

142．Sine theorem （law of sines）202

143．Cosine theorem （law of cosines）202

144．Theorem204

145．Given the three sides to find the angles204

146．Given the three angles to find the sides205

147．Napier＇s analogies206

148．Gauss＇s equations208

149．Rules for species in oblique spherical triangles209

150．Cases210

151．Case Ⅰ．Given the three sides to find the three angles211

152．Case Ⅱ．Given the three angles to find the three sides212

153．Case Ⅲ．Given two sides and the included angle212

154．Case Ⅳ．Given two angles and the included side213

155．Case Ⅴ．Given two sides and the angle opposite one of them213

156．Case Ⅵ．Given two angles and the side opposite one of them215

157．Area of a spherical triangle215

158．L＇Huilier＇s formula216

159．Definitions and notations217

160．The terrestrial triangle217

161．Applications to astronomy218

162．Fundamental points， circles of reference219

Summary of formulas222

Useful constants225

INDEX226

LOGARITHMS AND EXPLANATIONS OF TABLES240

1．Use of Logarithms240

2．Exponents240

3．Definitions241

4．Notation241

5．Systems of Logarithms242

6．Properties of Logarithms242

7．Logarithms to the Base 10243

8．Rules for Determining the Characteristic245

9．The Mantissa246

10．Tables246

11．To Find the Mantissa of the Logarithm of a Number247

12．Rules for Finding the Mantissa248

13．Finding the Logarithm of a Number249

14．To Find the Number Corresponding to a Logarithm249

15．Rules for Finding the Number Corresponding to a Given Loga-rithm251

16．To Multiply by Means of Logarithms252

17．To Divide by Means of Logarithms253

18．Cologarithms253

19．To Find the Power of a Number by Means of Logarithms254

20．To Find the Root of a Number by Means of Logarithms254

21．Proportional Parts255

22．Suggestions255

23．Changing Systems of Logarithms259

24．Use of Table Ⅱ260

25．Table Ⅲ．Explanatory262

26．To Find Logarithmic Function of an Acute Angle262

27．To Find the Acute Angle Corresponding to a Given LogarithmicFunction263

28．Angles near 0 and 90°265

29．Functions by Means of S and T265

30．Functions of Angles Greater Than 90°266

31．Table Ⅳ．Explanatory268

32．To Find the Natural Function of an Angle268

33．To Find the Angle Corresponding to a Given Natural Function269

34．Table Ⅴ．Explanatory270

35．Errors of Interpolation271

Table Ⅰ．Logarithms of Numbers274

Table Ⅱ．Conversion of Logarithms295

Table Ⅲ．Logarithms of Trigonometric Functions296

Table Ⅳ．Natural Trigonometric Functions348

Table Ⅴ．Radian Measure372

Table Ⅵ．Constants and Their Logarithms373