# Plane and Spherical Trigonometry: An Elementary Text-book

Scribner's, 1902 - Trigonometry - 157 pages
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### Contents

 Heights and distances 19 CHAPTER III 24 Theorem 25 Angles 26 The measure of angles 27 Addition of directed angles 29 F ᎪᎡᎢ 15 Angles between directed lines 30 Functions of angles of any magnitude 31 0 32 Algebraic signs of the functions 33 Functions of the quadrantal angles 35 Line values of the functions 38 Variations of the functions 39 CHAPTER IV 45 3 46 Functions of 47 2 48 Reduction of the functions of any angle to functions of an angle less than π π 4 α π α + π 50 Projection 52 Projection of a broken line 53 Projections on the axes of any line through the origin 27 Projections of any line on the axes 54 Functions of the sum and difference of two angles 56 PAGE 61 1 62 9 63 13 64 16 66 Sum and difference of the sines and of the cosines of two angles 69 19 71 CHAPTER V 72 27 76 Inverse trigonometric functions 77
 33 93 Solution of oblique triangles 45 Case I Given two angles and one side 95 Case II Given two sides and the included angle CHAPTER VI 97 Solution by logarithms 98 Case III Given two sides and the angle opposite one of them 99 Case IV Given the three sides 103 Solution by logarithms 104 35 105 39 106 Area of an oblique triangle 107 45 108 50 111 52 117 53 119 Introduction 53 Right triangles 120 54 122 Solution of right triangles 123 56 126 Quadrantal triangles 127 CHAPTER VIII 128 59 130 Napiers analogies 133 64 135 69 139 72 141 76 142 81 149 8885 89 90 92 25558 92 153 104 154 117 155 129 156 Copyright

### Popular passages

Page 120 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 97 - Two sides of a triangle, and the angle opposite one of them, being given, to describe the triangle. Let A and B be the given sides, and C the given angle.
Page xiii - COR. 2. Two right triangles are similar if an acute angle of the one is equal to an acute angle of the other.
Page 88 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 107 - ... 12. Looking out of a window with his eye at the height of 15 ft. above the roadway, an observer finds that the angle of elevation of the top of a telegraph post is 17� 18' 35", and that the angle of depression of the foot of the post is 8� 32
Page 18 - The angle of elevation of the top of a tower from a point P on the ground is 60�.
Page 110 - The angle of elevation of a tower at a distance of 20 yd. from its foot is three times as great as the angle of elevation 100 yd.
Page 110 - Find the trigonometric functions of 48�. [HINT : 48� = 30� + 18�.] 12. Two parallel chords of a circle lying on the same side of the centre of a circle subtend angles of 72� and 144� at the centre. Show that the distance between the chords is equal to half the radius of the circle, (a) using tables, (6) not using tables.
Page 88 - The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.
Page 87 - Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...