ART.

INTRODUCTION

PLANE TRIGONOMETRY

CONTENTS

CHAPTER I. THE TRIGONOMETRIC FUNCTIONS OF ANY

ANGLE AND IDENTICAL RELATIONS AMONG THEM

1. Rectangular coördinates.

2. Angles of any magnitude

3. Abscissa, ordinate, and distance

4-5. The trigonometric functions defined

6. Signs of the functions

7. Functions of acute angles

8. Reciprocal functions

9. Tangent, sine, and cosine

10. Sine and cosine

11. Tangent and secant .

12-13. Fundamental relations, collected

14. Values of the functions when one is given

CHAPTER II. IDENTICAL RELATIONS AMONG THE FUNC-

THE VALUES OF THE

TIONS OF RELATED ANGLES.

FUNCTIONS OF CERTAIN ANGLES

25-26. Functions of 90°, etc.

27. Limiting values of functions

ix

ART.

CHAPTER III. THE SOLUTION OF RIGHT TRIANGLES.

LOGARITHMS AND COMPUTATION BY MEANS OF

LOGARITHMS

28. Solution of right triangles

29. Logarithms

20. The common system

31. Mantissa and characteristic

32. Four computation theorems

33. Special properties of logarithms

34-35. Illustrative examples .

CHAPTER IV.

FUNDAMENTAL IDENTITIES

36. Introductory

37-40. The addition formulæ, sine and cosine

41. The addition formulæ, tangent and cotangent

42-43. Functions of the double angle

44. Functions of the half angle

45. Sum of sines; sum of cosines.

46. Identities and equations.

CHAPTER V. THE CIRCULAR OR RADIAN MEASURE OF

AN ANGLE. INVERSE TRIGONOMETRIC FUNCTIONS

47. Circular or radian measure

48. Inverse functions

49. General value of an angle

CHAPTER VI. THE SOLUTION OF GENERAL TRIANGLES

50. Four cases

51. The law of sines

52. Case I; a side and two angles

53. Case II; two sides and an opposite angle

54-55. Case III; two sides and included angle

56. The law of cosines

57-59. Formulæ from the law of cosines

66. Case IV; three sides

61. Case III; other methods of solution

62. Areas of right triangles

63. Areas of oblique triangles

64. Introductory

65. Illustrative examples

CHAPTER VII. THE SOLUTION OF TRIGONOMETRIC
EQUATIONS

73. Special formulæ for right triangles ..

74. Special formulæ ; collected. Napier's rules

75. Rules for solution

76. Illustrative examples. Quadrantal triangles .

CHAPTER IX. THE SOLUTION OF RIGHT SPHERICAL

TRIANGLES

CHAPTER X. THE SOLUTION OF OBLIQUE SPHERICAL

TRIANGLES

୧

77. Six cases

78. Case 1.

Three sides

79. Case 2. Three angles

80. Case 3. Two sides, included angle. Case 4. Two
angles, included side. Napier's analogies

81. Illustrative examples

82. Case 5. Two sides, opposite angle. Case 6. Two

angles, opposite side .

83. Delambre's or Gauss's equations

84. Distances on the earth

85. Position and direction; latitude and longitude; course

86-87. Bearings; illustrative examples

88. Area of a triangle

ANSWERS

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