This is a schedule for a ~15 week course covering
rectangular and polar geometry in two-dimensional space,
“unit-circle” and “right triangle” trigonometry,
synthetic trigonometry, the law of sines and law of cosines,
and vector geometry in two- and three-dimensional space.
Within each section there are links to
textbook chapters, readings, video lectures,
Desmos demonstrations,
display notes, exercises and problems, and past midterm exams.
Chapters enumerated with § refer to
Trigonometry, 2nd Edition by Stewart, et al .
Topics marked like
are extracurricular and won’t appear on exams.
Prerequisite Topics
The Basics of Arithmetic and Algebra
Triangles and the Pythagorean Theorem
The Coordinate Geometry of Linear and Quadratic Equations
Graphing Lines by Solving for y and Plotting Points , Professor Leonard (Video)
Finding x and y Intercepts on a Graph , Professor Leonard (Video)
Graphing Lines with the Intercept Method , Professor Leonard (Video)
Horizontal and Vertical Lines , Professor Leonard (Video)
Introduction to the Slope of a Line , Professor Leonard (Video)
Discovering the Slope Formula , Professor Leonard (Video)
Finding the Slope of a Line Graphically , Professor Leonard (Video)
Using the Slope Formula Given Two Points , Professor Leonard (Video)
Graphing Lines Using a Point and the Slope , Professor Leonard (Video)
Introduction to Slope-Intercept Form , Professor Leonard (Video)
How to Use Slope-Intercept Form , Professor Leonard (Video)
Finding Equations of Parallel and Perpendicular Lines , Professor Leonard (Video)
Discovering Point-Slope Form , Professor Leonard (Video)
Using the Point-Slope Equation of a Line , Professor Leonard (Video)
Finding the Equation of a Line From Two Points , Professor Leonard (Video)
Introduction to Solving Quadratics , Professor Leonard (Video)
The Square Root Method in Solving Quadratics , Professor Leonard (Video)
Using Factoring to Solve Quadratics , Professor Leonard (Video)
Completing the Square Made Easy , Professor Leonard (Video)
Proving the Quadratic Formula , Professor Leonard (Video)
Using the Quadratic Formula , Professor Leonard (Video)
Graphing Quadratic Functions , Professor Leonard (Video)
Analytic Geometry: Functions and their Graphs
§C.1 Using a Graphing Calculator
Introduction to Functions , Professor Leonard (Video)
How to Evaluate Functions , Professor Leonard (Video)
Finding the Domain of Functions , Professor Leonard (Video)
Features of Graphs, Domain, Range , Professor Leonard (Video)
Introduction to Graph Transformations , Professor Leonard (Video)
How to Graph with Transformations , Professor Leonard (Video)
Operations of Functions , Professor Leonard (Video)
Composition of Functions , Professor Leonard (Video)
One to One Functions , Professor Leonard (Video)
Finding Inverse Functions , Professor Leonard (Video)
Week One · January 26
Tuesday – Rectangular Geometry Fundamentals
Thursday – Syllabus Synopsis + Early-Term Survey
Week Two · February 2
Tuesday – Angle Measure + Technology Demo
§3.1 Angle Measure
Angle , Wikipedia
Decimal degrees , Wikipedia
Minutes and seconds of an arc , Wikipedia
Radian , Wikipedia
Introduction to Angles , Professor Leonard (Video)
Converting Degrees, Minutes, and Seconds , Professor Leonard (Video)
Introduction to Radians , Professor Leonard (Video)
Converting Radians and Degrees , Professor Leonard (Video)
Thursday – Polar Geometry Fundamentals
Week Three · February 9
Tues/Thursday – “Unit Circle” Trigonometry
Week Four · February 16
Tuesday –
Navigation , Wikipedia
Geographic coordinate system , Wikipedia
Latitude , Wikipedia
Longitude , Wikipedia
Prime meridian , Wikipedia
International Meridian Conference , Wikipedia
Horizontal coordinate system , Wikipedia
Azimuth , Wikipedia
Zenith , Wikipedia
True north , Wikipedia
Bearing (navigation) , Wikipedia
Heading (navigation) , Wikipedia
Course (navigation) , Wikipedia
Thursday – First Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Five · February 23
Tuesday – “Right Triangle” Trigonometry
Thursday – Inverse Trigonometric (Cyclometric) Functions
Week Six · March 2
Tues/Thursday – The Law of Sines & Law of Cosines
Week Seven · March 9
Tuesday –
Thursday – Second Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Eight · March 16
Thursday – Graphs of Trigonometric Functions
Thursday – Trigonometric Identities
§4.1 Trigonometric Identities
§4.2 Addition and Subtraction Formulas
§4.3 Double-Angle, Half-Angle, Product-Sum Formulas
List of trigonometric identities , Wikipedia
Proofs of trigonometric identities , Wikipedia
Introduction to Using Trigonometric Identities , Professor Leonard (Video)
How to Prove Trigonometric Identities , Professor Leonard (Video)
Introduction to Sum and Difference Formulas , Professor Leonard (Video)
Using Sum and Difference Formulas , Professor Leonard (Video)
Proving the Double and Half Angle Formulas , Professor Leonard (Video)
How to Use the Double and Half Angle Formulas , Professor Leonard (Video)
How to Use Product to Sum and Sum to Product Formulas , Professor Leonard (Video)
Week Nine · March 23
Week Ten · March 30
Tuesday –
Thursday – Third Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Eleven · April 6
Tuesday – Vectors in Two-Dimensional Space
Thursday – The Dot Product & Projections
Week Twelve · April 13
Tuesday – Three-Dimensional Rectangular Geometry
Thursday – Vectors in Three-Dimensional Space
Week Thirteen · April 20
Tues/Thursday – The Cross Product & Areas
Week Fourteen · April 27
Tuesday – Lines and Planes in Three-Dimensional Space
Thursday – Distances Between Points, Lines, and Planes
Week Fifteen · May 4
Tuesday –
Geodesy , Wikipedia
History of geodesy , Wikipedia
Geographic coordinate system , Wikipedia
Geodetic coordinates , Wikipedia
Reference ellipsoid , Wikipedia
Vertical deflection , Wikipedia
World Geodetic System , Wikipedia
Rhumb line , Wikipedia
Spherical trigonometry , Wikipedia
Celestial navigation , Wikipedia
Celestial mechanics , Wikipedia
Thursday – Fourth Midterm Exam
Past Midterm Exams
Week Sixteen · May 11
Final Exam
References
Trigonometry | 2nd Edition
James Stewart, Lothar Redlin, Saleem Watson
Copyright 2013 CENGAGE
cengage.com/c/trigonometry-2e-stewart/9781111574482/
Trigonometry: A Unit Circle Approach | Eleventh Edition
Michael Sullivan
Copyright 2020 Pearson
pearson.com
Trigonometry
I. M. Gelfand, Mark Saul
Copyright 2001 I. M. Gelfand
DOI: 10.1007/978-1-4612-0149-6
Trigonometric Delights
Eli Maor
Copyright 1998 Princeton University Press
ISBN: 0-691-05754-0
103 Trigonometry Problems From the Training of the USA IMO Team
Titu Andreescu , Zuming Feng
Copyright 2005 Birkhäuser Boston
DOI: doi.org/10.1007/b139082
eBook ISBN: 978-0-8176-4432-1
Spherical Trigonometry with Naval and Military Applications
Lyman M. Kells, Willis F. Kern, James R. Bland
Copyright 1942 McGraw-Hill Book Company Inc.