Unit 1
Angles, Radians & the Unit Circle
- Degree and radian measure
- Arc length and sector area
- Unit-circle coordinates
- Reference angles
- Exact trigonometric values
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College Mathematics
MATH 113 — Trigonometry
A college trigonometry roadmap covering trigonometric functions, identities, equations, complex-number form, and polar/parametric ideas.
Course overview
A college trigonometry roadmap covering trigonometric functions, identities, equations, complex-number form, and polar/parametric ideas.
Math Aficionado uses this structure as a tutoring roadmap: lessons can be paced around the student's current level, school sequence, assignments, and assessment goals rather than forcing every student through the same timetable.
Units & topics
Unit 2
Trigonometric Functions
- Sine, cosine, and tangent
- Reciprocal functions
- Domains and ranges
- Signs by quadrant
- Geometric meaning of trig functions
Unit 3
Graphs & Transformations
- Amplitude and midline
- Period and frequency
- Phase shifts
- Vertical and horizontal transformations
- Graphing from equations and data
Unit 4
Inverse Trigonometric Functions
- Restricted domains
- Inverse sine, cosine, and tangent
- Exact inverse-trig values
- Compositions and identities
- Applications of inverse trigonometry
Unit 5
Trigonometric Identities
- Pythagorean identities
- Even/odd and reciprocal identities
- Sum and difference identities
- Double- and half-angle identities
- Identity verification
Unit 6
Trigonometric Equations
- Basic trig equations
- Equations using identities
- Multiple-angle equations
- General solutions
- Equations on restricted intervals
Unit 7
Complex Numbers & De Moivre
- Complex numbers in rectangular form
- Polar/trigonometric form
- Multiplication and powers in polar form
- De Moivre’s theorem
- Roots of complex numbers
Unit 8
Polar & Parametric Connections
- Parametric equations
- Eliminating parameters
- Polar coordinates and graphs
- Conversions between coordinate systems
- Geometric interpretation and modeling
Curriculum reference: University of Wisconsin–Madison Guide / Department of Mathematics. The page is an independent tutoring roadmap and is not an official course page of the source institution.
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