Conceptual Trigonometry Part I
Conceptual Trigonometry Part I
A Companion to S. L. Loney's Plane Trigonometry Part I
About the Book
This work contains conceptual solutions to the problems and exercises given in the text book of Plane Trigonometry by S. L. Loney's including variations of problems, solutions, methods and approaches.
These solutions strengthen and enliven the inherent multi-concepts to enrich the heritage set forth by S. L. Loney.
The present work will serve as a complete guide to private students reading the subject with few or no opportunities of instruction. This will save the time and lighten the work of Teachers as well.
This book helps in acquiring a better understanding of the basic principles of Plane Trigonometry and in revising a large amount of the subject matter quickly. Care has been taken, as in the forthcoming ones, to present the solutions with multi-concepts and beyond in a simple natural manner, in order to meet the difficulties which are most likely to arise, and to render the work intelligible and instructive.
About the Author
Table of Contents
1 Measurement of Angles
1.1 Sexagesimal and Centesimal Measure .
1.2 Circular Measure . . . . . . . . . . . . .
1.3 The Radian . . . . . . . . . . . . . . . . .
1.4 Measurement of Any Angle in Radians
2 Trigonometrical Ratios for Angles Less Than A Right Angle
2.1 Trigonometrical Ratios . . . . . . . . . . . . .
2.2 Relations and Trigonometrical Ratios . . . .
2.3 Values of Trigonometrical Ratios . .
3 Simple Problems in Heights and Distances
3.1 Simple Problems . .
4 Applications of Algebraic Signs to Trigonometry
4.1 Tracing the changes in the ratios . .
5 Trigonometrical Functions of Angles of Any Size and Sign
5.1 Angles of Any Size and Sign .
6 General Expressions for All Angles Having A Given Trigonometrical Ratio
6.1 Generic Values . . . . . . . . . . . . . . . . . . . . . . .
6.2 Trigonometrical Equations . .
7 Trigonometrical Ratios of The Sum and Difference of Two Angles
7.1 Addition and Subtraction Theorems . . . .
7.2 Product Formulae . . . . . . . . . . . . . . .
7.3 Converse Formulae . . . . . . . . . . . . . .
7.4 Tangent of The Sum of Two Angles . . . . .
8 The Trigonometrical Ratios of Multiple and Submultiple Angles
8.1 Multiple Angles . . . . . . . . . . . . . . . . . . . . . . .
8.2 Submultiple Angles . . . . . . . . . . . . . . . . . . . . .
8.3 Angles of 9 ◦ , 18 ◦ , 36 ◦ , 81 ◦ . . . . . . . . . . . . . . . . .
9 Identities And Trigonometrical Equations
9.1 Tangent of The Sum of Angles . . . . . . . . . . . . .
9.2 Identities . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Trigonometrical Equations . . . . . . . . . . . . . . . .
10 Logarithms
10.1 Characteristics, Mantissa and Properties . . . . . . . .
11 Tables of Logarithms And Trigonometrical Ratios, Principle of Proportional Parts
11.1 Proportional Parts . . . . . . . . . . . . . . . . . . . .
11.2 Logarithmic Sines, Tangents And Secants . . . .
12 Relations Between The Sides and The Trigonometrical Ratios of The Angles of Any Triangle
12.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2 Sides And Angles of A Triangle . . . . . . . . . . . . . .
13 Solution of Triangles
13.1 Solution of Right-Angled Triangles . . .
13.2 Solution of Non-Right-Angled Triangles
13.3 Two Sides and Included Angle . . . . .
13.4 Ambiguous Case . . . . . . . . . . . . .
13.5 One Side Two Angles vs. Three Angles
14 Heights and Distances
14.1 Inaccessible Object and Distant Points . . . . . . . . .
14.2 Angle Subtended at Two Points . . . . . . . . . . . . . .
15 Properties of A Triangle
15.1 Area of a Given Triangle . . . . . . . . . . . . . . . . . .
15.2 The Circles Connected With A Triangle . . . . . . . . .
15.3 Orthocenter and Pedal Triangle . . . . . . . . . . . . .
16 On Quadrilaterals And Regular Polygons
16.1 Area of a Quadrilateral . . . . . . . . . . . . . . . . . . .
16.2 Regular Polygons . . . . . . . . . . . . . . . . . . . . . .
17 Trigonometrical Ratios of Small Angles, Area of A Circle, DIP of The Horizon.
17.1 Ratios of Small Angles
17.2 Area of A Circle . . . .
17.3 Dip of The Horizon . .
18 Inverse Circular Functions
18.1 Identities and Equations . . . . . . . . . . . . . . . .
19 On Some Simple Trigonometrical Series
19.1 Simple Series . . . . . . . . . . . . . . . . . . . . . . . .
20 Elimination
20.1 Elimination of Unknown Quantity . . .
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