Plane Trigonometry

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Longmans, Green, and Company, 1906
 

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Continguts

Degree measure The protractor
18
Trigonometric ratios defined for acute angles
20
Definite and invariable connection between acute angles and trig onometric ratios
24
Practical problems
26
Trigonometric ratios of 45 60 30 0 90
31
Relations between the trigonometric ratios of an angle and those of its complement
32
Summary
37
Solution of Rightangled Triangles AKT PAGE 20 Solution of a triangle
38
The method of computation
39
Comparison between the graphical method and the method of computation
40
General directions for solving problems
41
Checks upon the accuracy of the computation
43
CHAPTER IV
49
Measurement of heights and distances
50
Problems requiring a knowledge of the points of the mariners compass
53
Mensuration
54
Solution of isosceles triangles
55
Solution of oblique triangles
57
34a Area of a triangle in terms of its sides
60
Distance and dip of the visible horizon
61
Summary
63
CHAPTER V
65
Trigonometric definition of an angle Angles unlimited in magni tude Positive and negative angles
67
Supplement and complement of an angle
69
The convention of signs on a plane
70
General definition of the trigonometric ratios
71
different quadrants
72
To represent the angle geometrically when the ratios are given
74
Connection between angles and trigonometric ratios
76
Relations between the trigonometric ratios of an angle
77
Ratios of 90 A 90 + A 180 A A
79
Trigonometric Ratios of the Sum and the Difference of Two Angles 46 Derivation of the sine and cosine of the sum of two angles when each of the a...
85
Case III Given two sides and their included angle
105
The aid of logarithms in the solution of triangles
106
The use of logarithms in Cases I II
107
Relation between the sum and the difference of any two sides of a triangle The law of tangents Use of logarithms in Case III
108
ART FAgB 62 Trigonometric ratios of the halfangles of a triangle Use of loga rithms in Case IV
110
Problems in heights and distances
113
Summary
115
Length of a side of a triangle in terms of the adjacent sides and the adjacent angles
116
Area of a triangle
117
Area of a quadrilateral in terms of its diagonals and their angle of intersection
118
The circumscribing circle of a triangle
119
The escribed circles of a triangle
120
CHAPTER IX
121
The value of a radian
122
The radian measure of an angle Measure of a circular arc
123
CHAPTER X
128
Algebraical note
129
Changes in the trigonometric functions as the angle increases from 0 to 360
131
Periodicity of the trigonometric functions
134
The old or line definitions of the trigonometric functions
135
Geometrical representation of the trigonometric functions
137
Graphical representation of functions
138
Graphs of the trigonometric functions
139
General Values Inverse Trigonometric Functions
146
Sum and difference of two antitangents Exercises on inverse
152
Functions of the sum of three angles
158
APPENDIX
165
On the ratio of the length of a circle to its diameter
171
Questions and Exercises for Practice and Review
181
Answers to the Examples
203
Relations between the radian measure the sine and the tangent
83
an angle 143
106

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Pàgina 52 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Pàgina 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Pàgina 108 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Pàgina 74 - The area of the surface of a sphere is four times the area of a great circle.
Pàgina 108 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Pàgina 72 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Pàgina 62 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F THE RIGHT TRIANGLE.
Pàgina 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Pàgina 200 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Pàgina 202 - Find the area of a regular polygon of n sides inscribed in a circle, and show, by increasing the number of sides of the polygon without limit, how the expression for the area of the circle may be obtained. 13. (a) Find the distance at which a building 50 ft. wide will subtend an angle of 3'. (6) A church spire 45 ft. high subtends an angle of 9

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