Page 1: Introduction
Trigonometry deals with relationships between sides and angles of right-angled triangle.
Trigonometric ratios: sin, cos, tan, cosec, sec, cot.
Chapter covers standard values, identities, and calculations.
Page 2: Right-Angled Triangle
Hypotenuse: longest side opposite right angle.
Opposite side: opposite to angle θ
Adjacent side: next to θ (not hypotenuse)
Page 3: Trigonometric Ratios
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Page 4: Standard Angles Values
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | undefined |
Memorise this table!
Page 5: Complementary Angles
sin(90° - θ) = cos θ
cos(90° - θ) = sin θ
tan(90° - θ) = cot θ
Page 6: Trigonometric Identities
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Derived from Pythagoras.
Page 7: Key Points Summary
- 6 ratios and reciprocal relations
- Standard table 0-90°
- Three fundamental identities
Page 8: Practice Questions - Easy (1-10)
- sin 30° value.
- cos 90°.
- tan 45°.
- sec 0°.
- cot 60°.
- sin(90° - 60°).
- Identity sin² + cos².
- tan θ = sin/cos.
- cosec 30°.
- tan 90°.
Page 9: Practice Questions - Medium (11-20)
- Prove sin²θ + cos²θ = 1 for 45°.
- Find tan 30° using values.
- sec²θ - tan²θ = ?
- Value of cos 60° + sin 30°.
- cot(90° - θ) = ?
- Prove 1 + tan²θ = sec²θ for 30°.
- Find all ratios for 45°.
- sin θ = 3/5, find cos θ.
- tan θ = 1/√3, find θ.
- cosec²θ - cot²θ = ?
Page 10: Practice Questions - Hard (21-30)
- Prove identity using Pythagoras.
- If sin θ = 4/5, find all ratios.
- Prove 1 + cot²θ = cosec²θ.
- Value of sin 18° hint (advanced).
- Board level identity verification.
- Find θ if tan θ = √3.
- Multiple angle value calculation.
- Prove complementary relations.
- Identity application numerical.
- Full table verification.
Page 11: Standard Table
Complete 0° to 90° table with all ratios.
Page 12: Identities Table
All three identities and reciprocal relations.
Page 13: Common Mistakes
- Wrong value for 30°/60°
- Forgetting square in identities
- Mixing sin and cos for complementary
- Undefined tan 90°
- Wrong reciprocal
Page 14: Previous Year Questions
Value of ratios, prove identities, find θ.
Page 15: Exam Tips
- Memorise table perfectly
- Quote identities correctly
- Show steps in proof
- Use complementary when possible
- Practice all values
Page 16: Quick Revision Sheet
Table, identities, relations.
Page 17: Final Motivation
Chapter 8 complete! Trigonometry starts here — master the table!
Next chapter applications will be easier.
Class 10 Maths unstoppable 🦖
Page 18: Extra Practice Values
More calculations.
Page 19: Identity Proofs
Step-by-step.
Page 20: Complementary Angles
Detailed examples.
Page 21: Board Pattern Questions
Common types.
Page 22: Extra Questions
More practice.
Page 23: Ratio Diagram
Right triangle labelling.
Page 24: Reciprocal Relations
All pairs.
Page 25: Memorisation Trick
Table mnemonics.
Page 26: Common Values Table
Repeated for revision.
Page 27: Thank You & Copyright
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