Unit 1
Angles, Radians & the Unit Circle
- Degree and radian measure
- Coterminal and reference angles
- Arc length
- Unit-circle coordinates
- Exact trigonometric values
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School Mathematics · Grades 6–12
Trigonometry
A focused trigonometry course covering angle measure, unit-circle definitions, graphs, identities, equations, inverse functions, triangle applications, and advanced representations.
Course overview
This roadmap is designed as a dedicated trigonometry course or bridge between Algebra 2 and precalculus. Its structure closely reflects the content of UW–Madison MATH 113 while remaining appropriate for secondary students.
Math Aficionado uses this structure as a tutoring roadmap rather than a fixed school syllabus. Lessons can be reordered around the student's current unit, teacher materials, placement level, assignments, and assessment goals.
Units & topics
Unit 2
Right-Triangle Trigonometry
- Sine, cosine and tangent
- Reciprocal functions
- Solving right triangles
- Angles of elevation and depression
- Applications and modeling
Unit 3
Trigonometric Functions & Graphs
- Sine, cosine and tangent graphs
- Amplitude, period and phase shift
- Vertical and horizontal transformations
- Graphs of reciprocal functions
- Modeling periodic phenomena
Unit 4
Inverse Trigonometric Functions
- Inverse sine, cosine and tangent
- Restricted domains and principal values
- Evaluating inverse trig expressions
- Compositions and identities
- Applications to angle measurement
Unit 5
Fundamental Identities
- Pythagorean identities
- Reciprocal and quotient identities
- Even and odd identities
- Simplifying trigonometric expressions
- Strategy for identity verification
Unit 6
Trigonometric Equations
- Linear trig equations
- Factoring and substitution
- Equations using identities
- General solutions
- Equations on specified intervals
Unit 7
Angle-Sum & Multiple-Angle Identities
- Sum and difference formulas
- Double-angle identities
- Half-angle identities
- Power-reduction ideas
- Identity-based applications
Unit 8
General Triangles
- Law of Sines
- Law of Cosines
- Area formulas involving sine
- Ambiguous SSA cases
- Surveying and navigation applications
Unit 9
Polar, Parametric & Complex Representations
- Parametric equations and motion
- Polar coordinates and graphs
- Converting between coordinate systems
- Complex numbers in trigonometric form
- De Moivre-style applications
Unit 10
Trigonometric Modeling & Readiness
- Periodic data models
- Harmonic and phase analysis
- Vector and geometric applications
- Technology-assisted graphing
- Precalculus and calculus readiness
How the roadmap is aligned
UW–Madison MATH 113: Trigonometry and Wisconsin high-school Geometry/Functions standards. UW–Madison describes MATH 113 as covering trigonometric graphs, identities, equations, complex-number trigonometric form, polar and parametric equations.
This is an independent tutoring roadmap, not an official UW–Madison or Wisconsin Department of Public Instruction course. Wisconsin standards are used as the K–12 framework; current UW–Madison course descriptions are used where the pathway overlaps with college-level precalculus and calculus preparation.
Wisconsin Standards for Mathematics (2021) · UW–Madison Mathematics Course Guide
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