This is a schedule for a ~15 week course covering
rectangular and polar geometry in two-dimensional space,
“unit-circle” trigonometry and “right triangle” trigonometry,
synthetic trigonometry in general up to the laws of sines and cosines,
a touch of analytic trigonometry,
and the trigonometric aspects of vector geometry
in two- and three-dimensional space.
Within each section there are links to
textbook chapters, recommended readings, video lectures
Desmos demonstrations,
display notes, exercises and problems, and past midterm exams.
Chapters enumerated with § refer to
Trigonometry, 2nd Edition
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 LeonardFinding x and y Intercepts on a Graph , Professor LeonardGraphing Lines with the Intercept Method , Professor LeonardHorizontal and Vertical Lines , Professor LeonardIntroduction to the Slope of a Line , Professor LeonardDiscovering the Slope Formula , Professor LeonardFinding the Slope of a Line Graphically , Professor LeonardUsing the Slope Formula Given Two Points , Professor LeonardGraphing Lines Using a Point and the Slope , Professor LeonardIntroduction to Slope-Intercept Form , Professor LeonardHow to Use Slope-Intercept Form , Professor LeonardFinding Equations of Parallel and Perpendicular Lines , Professor LeonardDiscovering Point-Slope Form , Professor LeonardUsing the Point-Slope Equation of a Line , Professor LeonardFinding the Equation of a Line From Two Points , Professor LeonardIntroduction to Solving Quadratics , Professor LeonardThe Square Root Method in Solving Quadratics , Professor LeonardUsing Factoring to Solve Quadratics , Professor LeonardCompleting the Square Made Easy , Professor LeonardProving the Quadratic Formula , Professor LeonardUsing the Quadratic Formula , Professor LeonardGraphing Quadratic Functions , Professor Leonard
Analytic Geometry: Functions and their Graphs
§C.1 Using a Graphing Calculator
Introduction to Functions , Professor LeonardHow to Evaluate Functions , Professor LeonardFinding the Domain of Functions , Professor LeonardFeatures of Graphs, Domain, Range , Professor LeonardIntroduction to Graph Transformations , Professor LeonardHow to Graph with Transformations , Professor LeonardOperations of Functions , Professor LeonardComposition of Functions , Professor LeonardOne to One Functions , Professor LeonardFinding Inverse Functions , Professor Leonard
Week One · August 18
Tuesday – Rectangular Geometry Fundamentals
Thursday – Syllabus + Early-Term Assessment
Week Two · August 25
Tuesday – Angle Measure + Technology Demo
§3.1 Angle Measure
Angle , WikipediaDecimal degrees , WikipediaMinutes and seconds of an arc , WikipediaRadian , WikipediaIntroduction to Angles , Professor LeonardConverting Degrees, Minutes, and Seconds , Professor LeonardIntroduction to Radians , Professor LeonardConverting Radians and Degrees , Professor Leonard
Thursday – Polar Geometry Fundamentals
Week Three · September 1
Tues/Thursday – “Unit Circle” Trigonometry
Week Four · September 8
Tuesday –
Navigation , WikipediaGeographic coordinate system , WikipediaLatitude , WikipediaLongitude , WikipediaPrime meridian , WikipediaInternational Meridian Conference , WikipediaHorizontal coordinate system , WikipediaAzimuth , WikipediaZenith , WikipediaTrue north , WikipediaBearing (navigation) , WikipediaHeading (navigation) , WikipediaCourse (navigation) , Wikipedia
Thursday – First Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Five · September 15
Tuesday – “Right Triangle” Trigonometry
Thursday – Inverse Trigonometric (Cyclometric) Functions
Week Six · September 22
Tues/Thursday – The Law of Sines & Law of Cosines
Week Seven · September 29
Tuesday –
Thursday – Second Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Eight · October 6
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 , WikipediaProofs of trigonometric identities , WikipediaIntroduction to Using Trigonometric Identities , Professor LeonardHow to Prove Trigonometric Identities , Professor LeonardIntroduction to Sum and Difference Formulas , Professor LeonardUsing Sum and Difference Formulas , Professor LeonardProving the Double and Half Angle Formulas , Professor LeonardHow to Use the Double and Half Angle Formulas , Professor LeonardHow to Use Product to Sum and Sum to Product Formulas , Professor Leonard
Week Nine · October 13
Tuesday –
Thursday – Third Midterm Exam
Past Midterm Exams
The order of topics in this course has changed slightly since 2025Spring.
Week Ten · October 20
Tuesday – Vectors in Two-Dimensional Space
Thursday – The Dot Product & Projections
Week Eleven · October 27
Tuesday – Three-Dimensional Rectangular Geometry
Thursday – Vectors in Three-Dimensional Space
Week Twelve · November 3
Tues/Thursday – The Cross Product & Areas
Week Thirteen · November 10
Tuesday – Lines and Planes in Three-Dimensional Space
Thursday – Distances Between Points, Lines, and Planes
Week Fourteen · November 17
Tuesday –
Geodesy , WikipediaHistory of geodesy , WikipediaGeographic coordinate system , WikipediaGeodetic coordinates , WikipediaReference ellipsoid , WikipediaVertical deflection , WikipediaWorld Geodetic System , WikipediaRhumb line , WikipediaSpherical trigonometry , WikipediaCelestial navigation , WikipediaCelestial mechanics , Wikipedia
Thursday – Fourth Midterm Exam
Past Midterm Exams
Week Fifteen · November 24
Thanksgiving Break, No Class
Week Sixteen · December 1
Final Exam
Thursday December 11 @ 10am
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.