Exact Trigonometric Calculator

Understanding Exact Trigonometric Values

Common Exact Values

Special Angles (in degrees)

  • 0°: sin=0, cos=1, tan=0
  • 30°: sin=1/2, cos=√3/2, tan=1/√3
  • 45°: sin=1/√2, cos=1/√2, tan=1
  • 60°: sin=√3/2, cos=1/2, tan=√3
  • 90°: sin=1, cos=0, tan=undefined

Advanced Properties

Pythagorean Identities

  • sin²θ + cos²θ = 1
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = csc²θ

Periodicity

  • sin(θ + 2π) = sin θ
  • cos(θ + 2π) = cos θ
  • tan(θ + π) = tan θ

Cofunction Relations

  • sin(π/2 - θ) = cos θ
  • cos(π/2 - θ) = sin θ
  • tan(π/2 - θ) = cot θ

Applications

Real-world Usage

  • Navigation & GPS
  • Engineering Design
  • Wave Analysis
  • Architecture

Mathematical Applications

  • Complex Analysis
  • Fourier Series
  • Differential Equations
  • Vector Analysis

Advanced Topics

  • Hyperbolic Functions
  • Inverse Functions
  • Series Expansions
  • Complex Trigonometry