Trigonometric Functions — Concept Maps
Punjab Board · Class 11 · Mathematics
3 concept maps of Trigonometric Functions for Punjab Board Class 11 Mathematics, each also written out as a text outline.
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Trigonometric Functions - Comprehensive Overview
The map in words
- Trigonometric Functions
- Angle Measurement
- Degrees
- Conversion
- Minutes and Seconds
- Radians
- Arc Length Method
- Conversion from Degrees
- Relationship
- 180 degrees = pi radians
- Complete Revolution = 2pi
- Degrees
- Basic Functions
- Sine and Cosine
- Unit Circle Definition
- Pythagorean Identity
- Periodicity 2pi
- Tangent and Cotangent
- Ratio Definitions
- Periodicity pi
- Domain Restrictions
- Secant and Cosecant
- Reciprocal Functions
- Domain Restrictions
- Range Properties
- Sine and Cosine
- Identities and Formulas
- Sum and Difference
- x+y
- x-y
- x+y
- Double Angle
- sin(2x) = 2sinx cosx
- cos(2x) = cos²x - sin²x
- 2x) = 2tanx/(1-tan²x
- Half Angle
- From double angle
- sin²(x/2) from cos x
- cos²(x/2) from cos x
- Triple Angle
- sin(3x) = 3sinx - 4sin³x
- cos(3x) = 4cos³x - 3cosx
- tan(3x) formula
- Sum and Difference
- Applications
- Sum to Product
- Convert sums to products
- Simplify expressions
- Product to Sum
- Reverse conversion
- Simplify equations
- Solving Equations
- Use periodicity
- Find general solutions
- Check domain restrictions
- Sum to Product
- Function Analysis
- Domain and Range
- Sine and Cosine
- Tangent and Cotangent
- Secant and Cosecant
- Periodicity
- 2pi for sin cos sec csc
- pi for tan cot
- Symmetry
- Even functions
- Odd functions
- Quadrant signs
- Domain and Range
- Angle Measurement
Trigonometric Functions - Concept Overview
The map in words
- Trigonometric Functions
- Angle Measurement
- Degrees
- Radians
- Conversion Formulas
- Unit Circle Definition
- sin x, cos x
- tan x, cot x
- sec x, csc x
- Properties
- Domain and Range
- Periodicity
- Even and Odd Functions
- Signs in Quadrants
- Identities
- Fundamental Identity
- Sum Formulas
- Double Angle
- Triple Angle
- Product-to-Sum
- Sum-to-Product
- Applications
- Physics Waves
- AC Circuits
- Navigation
- Signal Processing
- Seismology
- Angle Measurement
Flowchart showing how angles are formed through ray rotation and how the direction determines the sign of the angle
The map in words
- Angle Formation
- Ray Rotation About Vertex
- Direction of Rotation?
- Anticlockwise: Positive Angle
- Example: 45°
- Clockwise: Negative Angle
- Example: -30°
- Anticlockwise: Positive Angle
- Direction of Rotation?
- Ray Rotation About Vertex
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