An Angle in Trigonometry

• 1. Preface
  • 1.1. Why I Wrote This Book?
  • 1.2. How to Read This Book?
  • 1.3. Who Should Read This Book?
  • 1.4. Prerequisite
  • 1.5. Goals for Readers
  • 1.6. Acknowledgments
• 2. Measurement of Angles
  • 2.1. Angle in Geometry
  • 2.2. Angle in Trigonometry
  • 2.3. Quadrants
  • 2.4. Units of Measurement
  • 2.5. Problems
• 3. Measurement of Angles Solutions
• 4. Trigonometrical Ratios
  • 4.1. Relationship betweeen Trigonometrical Functions or Ratios
  • 4.2. Problems
• 5. Trigonometrical Ratios Solutions
• 6. Trigonometrical Ratios of Angle and Sign
  • 6.1. Values of Trigonometrical Ratios for Some Useful Angles
  • 6.2. Complementary Angles
  • 6.3. Supplementary Angles
  • 6.4. Angles of $-\theta$
  • 6.5. Angles of $90^\circ -\theta$ and $90^\circ+\theta$
  • 6.6. Angles of $180^\circ + \theta$
  • 6.7. Angles of $360^\circ + \theta$
  • 6.8. Problems
• 7. Trigonometrical Ratios of Angle and Sign Solutions
• 8. Compound Angles
  • 8.1. The Addition Formula
  • 8.2. The Subtraction Formula
  • 8.3. Important Deductions
  • 8.4. To express $a\cos\theta + b\sin\theta$ in the form of $k\cos\phi$ or $k\sin\phi$
  • 8.5. Problems
• 9. Compound Angles Solutions
• 10. Transformation Formulae
  • 10.1. Transformation of products into sums or differences
  • 10.2. Transformation of sums or differences into products
  • 10.3. Problems
• 11. Transformation Formulae Solutions
• 12. Multiple and Submultiple Angles
  • 12.1. Multiple Angles
  • 12.2. Submultiple Angles
  • 12.3. Problems
• 13. Multiple and Submultiple Angles Solutions
• 14. Trigonometrical Identities
• 15. Trigonometrical Identities Solutions
• 16. Properties of Triangles
  • 16.1. Sine Formula or Sine Rule or Law of Sines
  • 16.2. Tangent Rule
  • 16.3. Cosine Formula or Cosine Rule
  • 16.4. Projection Formula
  • 16.5. Sub Angle Rules
  • 16.6. Sines of Angles in Terms of Sides
  • 16.7. Area of a Triangle
  • 16.8. Tangent and Cotangent of Sub-angles of a Triangle
  • 16.9. Dividing a Side in a Ratio
  • 16.10. Results Related with Circum Circle
  • 16.11. Results Related with In-Circle
  • 16.12. Results Related with Escribed Circles
  • 16.13. Distannces of Circum-center, In-center, Orthocenter and Centroid from Vertices
  • 16.14. Esccribed Triangles
  • 16.15. Distance between Orthocenter and Circumcenter
  • 16.16. Distance between Incenter and Circumcenter
  • 16.17. Area of a Cyclid Quadrilateral
• 17. Properties of Triangles’ Problems
• 18. Properties of Triangles’ Solutions Part 1
• 19. Properties of Triangles’ Solutions Part 2
• 20. Properties of Triangles’ Solutions Part 3
• 21. Properties of Triangles’ Solutions Part 4
• 22. Properties of Triangles’ Solutions Part 5
• 23. Trigonometrical Equations and their General Solutions
  • 23.1. Trigonometrical Equation
  • 23.2. Solution of a Trigonometrical Equation
  • 23.3. General Solution
  • 23.4. Principal Value
  • 23.5. Tips for Finding Complete Solution
  • 23.6. Problems
• 24. Trigonometrical Equations and their General Solutions Answers
• 25. Inverse Circular Functions
  • 25.1. Principal Value
  • 25.2. Important Formulae
  • 25.3. Graph of Important Inverse Trigonometric Functions
  • 25.4. Problems
• 26. Inverse Circular Functions Solutions
• 27. Height and Distance
  • 27.1. Some Useful Properties of a Circle
  • 27.2. Problems
• 28. Height and Distance Solutions Part 1
• 29. Height and Distance Solutions Part 2
• 30. Height and Distance Solutions Part 3
• 31. Height and Distance Solutions Part 4
• 32. Height and Distance Solutions Part 5
• 33. Periodicity of Trigonometrical Functions
  • 33.1. Problems
  • 33.2. Solutions
• 34. Graph of Trigonometric Functions
  • 34.1. Problems
  • 34.2. Solutions

Indices and tables

• Index