Detailed Summary
Trigonometry is a branch of mathematics that explores the relationships between the angles and sides of triangles, particularly right triangles. This section begins by illustrating real-life scenarios where trigonometric principles can be applied to measure heights and distances without direct measurement. Trigonometric ratios (
$$\sin \theta$$, $$\cos \theta$$, $$\tan \theta$$) based on the angles of right triangles are defined, alongside their reciprocals ($$\csc \theta$$, $$\sec \theta$$, $$\cot \theta$$). The historical success of trigonometry in astronomy and engineering is also highlighted, emphasizing its importance in advanced mathematical applications.
The discussion includes the values of trigonometric ratios for specific angles (0°, 30°, 45°, 60°, and 90°), establishing foundational knowledge necessary for resolving more complex trigonometric identities. A critical section of the chapter is dedicated to proving fundamental identities such as $$\sin^2 A + \cos^2 A = 1$$, enabling a deeper understanding of the relationships within trigonometric equations. Additionally, students are presented with exercises and examples to apply their understanding, paving the way for further exploration in trigonometry.