Trigonometri | 5. Ders | 10. Sınıf Matematik Konu Anlatımı | 1. Tema | Maarif Model | TAF-10

Zihin haritası özeti: Trigonometric Special Angles

30-60-90 Triangle
- Side Ratios
  - Opposite 30: 1 unit
  - Opposite 60: √3 unit
  - Opposite 90: 2 units
- Sine Values
  - sin 30° = 1/2
  - sin 60° = √3/2
- Cosine Values
  - cos 30° = √3/2
  - cos 60° = 1/2
- Tangent & Cotangent
  - tan 30° = 1/√3
  - cot 30° = √3
45-45-90 Triangle
- Equal Legs
  - Opposite 45: 1 unit
- Hypotenuse
  - Equals √2
- Sine & Cosine
  - sin 45° = √2/2
  - cos 45° = √2/2
- Tangent & Cotangent
  - tan 45° = 1
  - cot 45° = 1
Complementary Angles
- sin θ = cos(90°-θ)
  - sin 30° = cos 60°
  - sin 60° = cos 30°
- tan θ = cot(90°-θ)
  - tan 30° = cot 60°
  - tan 60° = cot 30°
Memorization Table
- 0-1-2-3-4 Method
  - Write numbers
  - Take square roots
  - Divide by 2
- Special Angles
  - 0°, 30°, 45°, 60°, 90°
- Sine Row Results
  - sin 0° = 0, sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2, sin 90° = 1
Tangent Special Cases
- tan θ = sin θ/cos θ
  - tan 0° = 0
  - tan 45° = 1
  - tan 60° = √3
  - tan 90° = undefined
- Complementary Tangents
  - 90° pairs have reciprocal relationships
Application Problems
- Function Evaluation
  - Substitute angle values
  - Calculate using ratios
- Rational vs Irrational
  - Identify rational results
  - Exclude √2, √3 terms
- Right Triangle Geometry
  - Shadow length calculations
  - Building height problems
- Light Reflection
  - Angle of incidence = reflection
  - Mirror geometry setup
- Lighthouse Navigation
  - Angle of elevation
  - Distance calculations
  - Speed & time problems

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