Circular Functions
Circular Functions
Circular Functions
what you'll learn
Lesson details
Units 1 & 2 (Circular Functions)
Explore the unit circle definition of trigonometric functions, their algebraic representations, and graphical behavior. Emphasis is placed on understanding sine, cosine, and tangent as periodic functions, solving trigonometric equations, and applying these functions in modelling and geometric contexts.
Unit 2: Circular Functions and Their Applications
2.1 Unit Circle and Radian Measure
Definition of Radian: arc length over radius
Converting Between Degrees and Radians
Unit Circle Values: exact values for sine and cosine at standard angles (0, π/6, π/4, π/3, π/2, etc.)
Symmetry and Periodicity on the Unit Circle
2.2 Graphing Circular Functions
Graphs of Sine, Cosine, and Tangent: domain, range, amplitude, period, axis
Transformations: vertical shifts, amplitude changes, period changes via horizontal compression/stretch, and phase shifts
Identifying Graph Features: intercepts, maxima/minima, asymptotes (for tangent), period cycles
2.3 Solving Trigonometric Equations
Using Unit Circle to Solve: sin(θ) = a, cos(θ) = b, tan(θ) = c
General Solutions: expressing all solutions using periodicity (e.g. θ = α + 2nπ)
Solving Equations Graphically: using technology to approximate where algebraic methods fail
2.4 Applications and Modelling
Modelling Periodic Phenomena: tides, seasonal variation, circular motion
Phase Shift Interpretation: delay/advance in periodic behaviour
Solving Problems in Context: interpreting and applying sine/cosine models to real-world scenarios (e.g. Ferris wheels, pendulums)
Units 1 & 2 (Circular Functions)
Explore the unit circle definition of trigonometric functions, their algebraic representations, and graphical behavior. Emphasis is placed on understanding sine, cosine, and tangent as periodic functions, solving trigonometric equations, and applying these functions in modelling and geometric contexts.
Unit 2: Circular Functions and Their Applications
2.1 Unit Circle and Radian Measure
Definition of Radian: arc length over radius
Converting Between Degrees and Radians
Unit Circle Values: exact values for sine and cosine at standard angles (0, π/6, π/4, π/3, π/2, etc.)
Symmetry and Periodicity on the Unit Circle
2.2 Graphing Circular Functions
Graphs of Sine, Cosine, and Tangent: domain, range, amplitude, period, axis
Transformations: vertical shifts, amplitude changes, period changes via horizontal compression/stretch, and phase shifts
Identifying Graph Features: intercepts, maxima/minima, asymptotes (for tangent), period cycles
2.3 Solving Trigonometric Equations
Using Unit Circle to Solve: sin(θ) = a, cos(θ) = b, tan(θ) = c
General Solutions: expressing all solutions using periodicity (e.g. θ = α + 2nπ)
Solving Equations Graphically: using technology to approximate where algebraic methods fail
2.4 Applications and Modelling
Modelling Periodic Phenomena: tides, seasonal variation, circular motion
Phase Shift Interpretation: delay/advance in periodic behaviour
Solving Problems in Context: interpreting and applying sine/cosine models to real-world scenarios (e.g. Ferris wheels, pendulums)
Units 1 & 2 (Circular Functions)
Explore the unit circle definition of trigonometric functions, their algebraic representations, and graphical behavior. Emphasis is placed on understanding sine, cosine, and tangent as periodic functions, solving trigonometric equations, and applying these functions in modelling and geometric contexts.
Unit 2: Circular Functions and Their Applications
2.1 Unit Circle and Radian Measure
Definition of Radian: arc length over radius
Converting Between Degrees and Radians
Unit Circle Values: exact values for sine and cosine at standard angles (0, π/6, π/4, π/3, π/2, etc.)
Symmetry and Periodicity on the Unit Circle
2.2 Graphing Circular Functions
Graphs of Sine, Cosine, and Tangent: domain, range, amplitude, period, axis
Transformations: vertical shifts, amplitude changes, period changes via horizontal compression/stretch, and phase shifts
Identifying Graph Features: intercepts, maxima/minima, asymptotes (for tangent), period cycles
2.3 Solving Trigonometric Equations
Using Unit Circle to Solve: sin(θ) = a, cos(θ) = b, tan(θ) = c
General Solutions: expressing all solutions using periodicity (e.g. θ = α + 2nπ)
Solving Equations Graphically: using technology to approximate where algebraic methods fail
2.4 Applications and Modelling
Modelling Periodic Phenomena: tides, seasonal variation, circular motion
Phase Shift Interpretation: delay/advance in periodic behaviour
Solving Problems in Context: interpreting and applying sine/cosine models to real-world scenarios (e.g. Ferris wheels, pendulums)
About Author
Theo – Tutor Summary
Specialty: Mathematical Methods
ATAR: 99.65
School: Xavier College Alumni
Subject Achievements:
50 Raw in Global Politics
47 Raw in History Revolutions
47 Raw in Mathematical Methods
44 Raw in English
Theo – Tutor Summary
Specialty: Mathematical Methods
ATAR: 99.65
School: Xavier College Alumni
Subject Achievements:
50 Raw in Global Politics
47 Raw in History Revolutions
47 Raw in Mathematical Methods
44 Raw in English
Theo – Tutor Summary
Specialty: Mathematical Methods
ATAR: 99.65
School: Xavier College Alumni
Subject Achievements:
50 Raw in Global Politics
47 Raw in History Revolutions
47 Raw in Mathematical Methods
44 Raw in English