Trigonometry

Trigonometry Curriculum

Trigonometry Curriculum

This curriculum provides a structured overview of the study of trigonometry.

Basic Trigonometry

Right Triangle Trigonometry:

  • Review of right triangles and Pythagorean Theorem
  • Definition of trigonometric functions (sin, cos, tan)
  • Cofunction identities
  • Values of trigonometric functions for special angles (30°, 45°, 60°)
  • Solving right triangles

Angles and Their Measures:

  • Degrees and radians
  • Conversion between degrees and radians
  • Arc length and sector area
  • Angular velocity and linear velocity
  • Applications of angles and their measures

Trigonometric Functions of Any Angle:

  • The unit circle
  • Trigonometric functions of any angle
  • Reference angles
  • Signs of trigonometric functions in different quadrants
  • Graphs of trigonometric functions (sin, cos, tan)

Advanced Trigonometry

Graphs of Trigonometric Functions:

  • Amplitude, period, and phase shift
  • Graphs of transformed trigonometric functions
  • Inverse trigonometric functions
  • Applications of trigonometric graphs
  • Damped trigonometric functions

Trigonometric Identities:

  • Basic trigonometric identities
  • Sum and difference formulas
  • Double-angle and half-angle formulas
  • Product-to-sum and sum-to-product formulas
  • Verifying trigonometric identities

Trigonometric Equations:

  • Solving trigonometric equations
  • General solutions and particular solutions
  • Solving trigonometric equations using identities
  • Applications of trigonometric equations
  • Solving trigonometric inequalities

Applications of Trigonometry

Law of Sines and Law of Cosines:

  • The Law of Sines
  • The Law of Cosines
  • Solving triangles using the Law of Sines and Law of Cosines
  • Applications to navigation, surveying, and other fields
  • Area of a triangle

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