Basics of Trigonometry

Introduction

• Trigonometry is the study of the ratios of sides of triangles.
• "Trig" means triangle, and "metry" means measure.

Right Triangle

• Definition of a right triangle: One angle is 90 degrees.
• Example:
  • Height: 3
  • Base: 4
  • Hypotenuse (longest side opposite the right angle): 5
• Pythagorean theorem:
  • 3² + 4² = 5²
  • 9 + 16 = 25 (validates the triangle)

Core Functions of Trigonometry

1. Sine (sin)
   • Ratio: opposite/hypotenuse
2. Cosine (cos)
   • Ratio: adjacent/hypotenuse
3. Tangent (tan)
   • Ratio: opposite/adjacent

Mnemonic: Soh Cah Toa

• Soh: Sine = Opposite / Hypotenuse
• Cah: Cosine = Adjacent / Hypotenuse
• Toa: Tangent = Opposite / Adjacent

Example Calculation for Angle Theta (θ)

• Opposite: 3
• Hypotenuse: 5
  • Sine of θ: sin(θ) = 3/5
• Adjacent: 4
  • Cosine of θ: cos(θ) = 4/5
  • Tangent of θ: tan(θ) = 3/4

Example Calculation for Angle X

• Redrawn Right Triangle:
  • Height: 3
  • Base: 4
  • Hypotenuse: 5
• For Angle X:
  • Opposite: 4
  • Sine of X: sin(x) = 4/5
  • Adjacent: 3
  • Cosine of X: cos(x) = 3/5
  • Tangent of X: tan(x) = 4/3

Conclusion

• Next video will cover more examples and explore functions for angles approaching 90 degrees and beyond.
• Soh Cah Toa concept is foundational but will evolve with angles greater than 90 degrees.