BASIC PRINCIPLES OF MATHEMATICS TABLE OF CONTENTS INTRODUCTION ..... 1 Chapter 1 1.1 DEFINITION ..... 2 1.2 TYPES OF TRIANGLES ..... 2 1.2.1 Arbitrary triangles ..... 2 1.3 GONIOMETRIC CIRCLE ..... 4 1.3.1 Arcs ..... 4 A. Complementary Arcs ..... 4 1.3.2 Angle a ..... 5 1.4 SINE AND COSINE ..... 7 1.4.1 The unity ..... 8 1.4.2.1 Sine ..... 11 1.5 TANGENT AND COTANGENT ..... 16 1.5.1 Signes ..... 17 1.5.1.1 Tangent ..... 18 1.6 SECANT ..... 22 1.6.1 Signes ..... 22 1.7 COSECANT ..... 24 1.7.1 Signes ..... 24 1.8 SUMMARY ..... 26 1.9 BASIC FORMULA ..... 27 1.10 OTHER IMPORTANT TRIGONOMETRIC FORMULAS ..... 28 1.11 TYPICAL TRIGONOMETRIC VALUES ..... 31 1.12 RIGHT ANGLED TRIANGLES ..... 32 1.12.1 Theorem I ..... 32 A. FURTHER COMMENTS ..... 34 1.13 TRIANGLES WITH NO RIGHT ANGLES ..... 37 1.13.1 Theorem I ..... 37 Chapter 2 2.1 DEFINITION ..... 39 2.2 PURPOSE OF SPHERICAL TRIGONOMETRY ..... 39 2.3 SPHERE ..... 39 2.3.1 Radius of a sphere ..... 39 2.4 GREAT CIRCLES AND SMALL CIRCLES ..... 41 2.4.1 Particularities relating to great circles ..... 42 2.5 SPHERICAL ANGLES ..... 44 2.6 SPHERICAL TRIANGLES ..... 45 2.7 FORMULAS ..... 46 2.7.1 Right angled spherical triangles ..... 46 2.7.1.1 Cosine Rule ..... 47 2.7.2 Spherical triangles with no right angles ..... 49 2.7.2.1 Group one ..... 49 Chapter 3 3.1 DEFINITION ..... 5 1 3.2 VERSINE ..... 51 Chapter 4 4.1 INTRODUCTION ..... 53 4.2 DEFINITION ..... 53 4.3 Pi ..... 53 4.4 RADIAN ..... 54 4.5 RELATION BETWEEN DEGREES AND RADIANS ..... 54 4.6 ABOUT DEGREES ..... 55 4.6.1 Degrees ..... 55 4.7 RADIANS ..... 57 4.8 USE OF RADIANS AND DEGREES ..... 57 4.8.1 Convert degrees to radians ..... 57 EXERCISES ..... 58 A. Area using degrees ..... 58 Chapter 5 5.1 INTRODUCTION ..... 60 5.2 DEFINITION ..... 60 5.3 TYPES OF LOGARITMS ..... 60 5.4 COMMON LOGARITMS ..... 61 5.5 STRUCTURE OF LOGARITHMS ..... 6 5.5.1 Index or characteristic ..... 63 5.5.1.1 Index of whole numbers ..... 63 5.6 USE OF THE TABLES OF LOGARITHMS ..... 66 5.6.1 Find the log corresponding to a given number ..... 66 5.6.1.1 The number consists of maximum 4 figures ..... 66 5.6.2 Find the number corresponding to a log ..... 67 5.6.2.1 The given logarithm is in the tables ..... 67 5.9 LOGARITHMS OF TRIGONOMETRICAL FUNCTIONS ..... 69 5.8 THE USE OF LOGARITHMS ..... 72 5.8.1 Worked examples ..... 72 5.8.1.1 Multiplications ..... 72 Right angled triangle ..... 74 |
