1. Introduction to Trigonometry  Definition and History of Trigonometry  Review on Angles and Triangles

2. Definition of Trigonometry Comes from the Greek word “trigonon” which means triangle and “metron” which means measure. Branch of mathematics that deals with the study of the relationships between the sides and angles of the triangle.

3. Branches of Trigonometry Plane Trigonometry – study of the relationships between angles and sides of triangle in two-dimensional plane/figure. Spherical Trigonometry – study of the relationships between angles and sides of triangle in three-dimensional plane/figure or in space.

4. A Brief History of Trigonometry Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flowered in the Gupta period, especially due to Aryabhata (6th century).

5. A Brief History of Trigonometry During the Middle Ages, the study of trigonometry continued in Islamic mathematics. It was adopted as a separate subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).

6. Review on Angles and Triangles Angles An angle is formed when two rays have the same endpoint. This endpoint is called the vertex. The two rays that form the angle are called sides.

7. Review on Angles and Triangles Kinds of Angles

8. Review on Angles and Triangles Triangles Simplest polygon with three vertices and three sides. The set of points inside the triangle is the interior or the triangular region. The set of points outside the triangle is the exterior of the triangle. The sum of the interior angles is 180° and the sum of the exterior angles is 360°.

9. Kinds of Triangles

10. Note: Equiangular Triangle – All angles are congruent and each angle is equal to 60°.