Trigonometry Basic Formulas

Trigonometry is a fundamental branch of mathematics that deals with the relationships between the angles and sides of a triangle. Understanding its basic formulas lays the foundation for solving complex problems in geometry, physics, and engineering. Below is a comprehensive guide on the most essential trigonometric formulas.

Basic Trigonometric Functions and Their Ratios

• Sine (sin θ) = Opposite side / Hypotenuse
• Cosine (cos θ) = Adjacent side / Hypotenuse
• Tangent (tan θ) = Opposite side / Adjacent side
• Cosecant (csc θ) = 1 / sin θ
• Secant (sec θ) = 1 / cos θ
• Cotangent (cot θ) = 1 / tan θ

Important Trigonometric Identities

• Pythagorean Identity: sin²θ + cos²θ = 1
• Reciprocal Identities:
  • csc θ = 1 / sin θ
  • sec θ = 1 / cos θ
  • cot θ = 1 / tan θ
• Quotient Identities:
  • tan θ = sin θ / cos θ
  • cot θ = cos θ / sin θ

Additional Notes

These formulas are critical in various fields like physics, astronomy, and computer science. Begin by practicing their application in solving triangles and continue exploring more advanced identities such as double-angle and half-angle formulas. For related topics, explore Advanced Trigonometric Identities and Applications of Trigonometry.