This presentation on Trigonometry introduces the fundamental concepts of the subject, including trigonometric ratios, values of standard angles, and important identities. It explains the graphical nature of trigonometric functions and highlights their real-life applications in measuring heights, distances, navigation, and engineering. With solved examples and visual explanations, the presentation aims to make trigonometry simple, practical, and engaging for learners.

1. Trigonometry
Exploring Ratios, Identities &
Applications

2. Introduction to Trigonometry
• • Trigonometry is the study of relationships
between the sides and angles of triangles.
• • Widely used in physics, engineering,
architecture, navigation, and astronomy.

3. Trigonometric Ratios
• In a right-angled triangle:
• • sin θ = Opposite / Hypotenuse
• • cos θ = Adjacent / Hypotenuse
• • tan θ = Opposite / Adjacent
• • cosec θ = 1/sin θ
• • sec θ = 1/cos θ
• • cot θ = 1/tan θ

4. Values of Standard Angles
• Standard angles: 0°, 30°, 45°, 60°, 90°
• sin θ: 0, 1/2, 1/√2, √3/2, 1
• cos θ: 1, √3/2, 1/√2, 1/2, 0
• tan θ: 0, 1/√3, 1, √3, ∞

5. Trigonometric Identities
• Fundamental Identities:
• • sin²θ + cos²θ = 1
• • 1 + tan²θ = sec²θ
• • 1 + cot²θ = cosec²θ

6. Graphs of Trigonometric Functions
• • The graphs of sine, cosine, and tangent are
periodic.
• • sin and cos oscillate between -1 and 1.
• • tan θ has vertical asymptotes where cos θ =
0.

7. Applications in Real Life
• • Measuring heights of buildings and
mountains.
• • Navigation and astronomy.
• • Engineering and construction.
• • Physics problems involving waves and
oscillations.

8. Sample Problems
• Example:
• A tower casts a shadow of 20 m when the
angle of elevation of the sun is 45°.
• Height of the tower = 20 × tan(45°) = 20 m.

9. Quick Recap
• • Trigonometry connects angles and sides of
triangles.
• • Key ratios: sin, cos, tan.
• • Standard values and identities simplify
calculations.
• • Useful in real-life applications like heights
and distances.

10. Thank You!
Questions?