Trigonometry - Concept map
Trigonometry
Related concepts
Angles and Measurements
Sub concepts
- Degrees and Radians
- Standard Position
- Coterminal Angles
- Reference Angles
- Quadrants
Relationship to central
Foundation for all trigonometric calculations
Unit Circle
Sub concepts
- Equation x² + y² = 1
- Coordinate Points
- Arc Length
- Terminal Points
Relationship to central
Core geometric foundation for trigonometric functions
Trigonometric Functions
Sub concepts
- Primary Functions (sin, cos, tan)
- Reciprocal Functions (csc, sec, cot)
- Function Values
- Domain and Range
Relationship to central
Primary tools for solving trigonometric problems
Special Angles
Sub concepts
- 30-60-90 Triangle
- 45-45-90 Triangle
- Common Angle Values
- Function Values Table
Relationship to central
Key reference values for calculations
Trigonometric Identities
Sub concepts
- Pythagorean Identities
- Reciprocal Identities
- Ratio Identities
- Sum and Difference Formulas
Relationship to central
Essential relationships for problem solving
Triangle Applications
Sub concepts
- Law of Sines
- Law of Cosines
- Law of Tangents
- Right Triangle Applications
Relationship to central
Real-world problem solving using trigonometric principles
Concept connections
- Unit CircleTrigonometric FunctionsProvides coordinate-based definitions for all trigonometric functions
- Special AnglesTrigonometric FunctionsGives exact values for commonly used angles
- Angles and MeasurementsUnit CircleDetermines position and coordinates on the circle
- Trigonometric IdentitiesTrigonometric FunctionsProvides relationships between different function values
- Triangle ApplicationsTrigonometric FunctionsApplies function values to solve real-world problems
- Special AnglesTriangle ApplicationsProvides exact values for solving triangle problems efficiently
- Trigonometric IdentitiesTriangle ApplicationsEnables algebraic manipulation in complex triangle problems
- Angles and MeasurementsSpecial AnglesProvides the measurement system for identifying special angle values
Diagrams
Complete Trigonometry Concept Map
Comprehensive overview of all trigonometry concepts showing hierarchical relationships between topics, subtopics, and specific formulas
Problem-Solving Decision Tree for Trigonometry
Step-by-step decision process for determining which trigonometric approach to use based on given information in triangle problems
Unit Circle Problem-Solving Steps
Systematic approach for solving unit circle problems, showing the logical sequence from angle identification to final answer
Distribution of Trigonometric Function Signs by Quadrant
Visual representation of how trigonometric function signs are distributed across the four quadrants of the coordinate plane
Converting Between Degrees and Radians
Clear conversion process between degree and radian measurements with formula applications and examples