Trigonometry

Overview of Trigonometry

• Definition: Derived from Greek trigonon (triangle) and metron (measure), trigonometry is the study of triangles, angles, and distances.
• Core Applications: Widely used in science, engineering, computer animation, and video game development to calculate missing distances or angles.
• Right-Angled Triangles: The primary focus of trigonometry. Sides are defined relative to an angle ($\theta$):
  • Adjacent: Next to the angle.
  • Opposite: Across from the angle.
  • Hypotenuse: The longest side.
• Primary Functions: Sine (sin), Cosine (cos), and Tangent (tan) represent ratios of triangle sides.
• The Unit Circle: A circle with a radius of 1 centered at 0, used to visualize and calculate trigonometric functions for any angle, including those beyond 360°.
• Measurement Units: Angles are measured in either Degrees or Radians (e.g., 90° = $\pi/2$ radians; 180° = $\pi$ radians).
• Repeating Patterns: Trigonometric functions are periodic; values repeat every full rotation (360° or $2\pi$ radians).
• Solving Triangles: Trigonometry allows for finding missing sides and angles in both right-angled and general triangles.
• Additional Functions:
  • Cosecant (csc): Hypotenuse / Opposite
  • Secant (sec): Hypotenuse / Adjacent
  • Cotangent (cot): Adjacent / Opposite
• Identities: Trigonometric and triangle identities are equations that remain true for all triangles, providing tools for complex calculations.