### Contents

 Solution by the aid of logarithms 18 Heights and distances 19 33 22 Directed lines 24 Theorem 25 Angles CHAPTER III 26 FUNCTIONS OF ANY ANGLE 13 The measure of angles 27 Addition of directed angles 29 Angles between directed lines 30 Functions of angles of any magnitude 31 Algebraic signs of the functions 33 Functions of the quadrantal angles 35 22222 37 Line values of the functions 38 Variations of the functions 39 CHAPTER IV 45 3 46 Functions of α π α 2 47 Reduction of the functions of any angle to functions of an π angle less than 4 50
 Inverse trigonometric functions 77 Solution of trigonometric equations 79 Trigonometric equations 81 Trigonometric equations 295 45 85 CHAPTER VI 89 Solution of oblique triangles 95 50 96 54 97 59 99 Case IV Given the three sides 103 PART II 117 Solution of right triangles 123 ᎪᎡᎢ 133 64 135 69 139 72 141 76 142 81 149 Copyright

### Popular passages

Page 122 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 91 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 99 - 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 1 - COR. 2. Two right triangles are similar if an acute angle of the one is equal to an acute angle of the other.
Page 90 - 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 109 - ... 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 20 - The angle of elevation of the top of a tower from a point P on the ground is 60�.
Page 56 - To find the sine and cosine of the sum and difference of two angles in terms of the sines and cosines of the angles themselves.
Page 112 - 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 112 - 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.