Trigonometry
Free Online Course • Self-Paced Learning • College-Level Trigonometry
Welcome to Your Trigonometry Learning Journey!
This comprehensive course covers the full scope of college-level trigonometry, from angles and the unit circle through identities, equations, and applications including vectors and polar coordinates. Each module includes detailed lessons, interactive practice problems, self-check quizzes, and comprehensive study materials.
Self-Paced
Learn on your schedule. All materials available 24/7.
Interactive
Practice problems with instant feedback and detailed solutions.
Comprehensive
Study guides, quick reference cards, and worked examples.
Research-Based
Designed using evidence-based learning principles.
Course Modules
Angles and Their Measure
Master angle measurement in degrees and radians, arc length, sector area, and angular speed.
- Degree measure and classifying angles
- Radian measure and converting between degrees and radians
- Arc length and area of a sector
- Angular and linear speed
The Unit Circle & Right Triangle Trig
Define sine and cosine on the unit circle, evaluate trig functions at special angles, and solve right triangles.
- Defining sine and cosine on the unit circle
- Evaluating trig functions at special angles
- Right triangle definitions of trig functions
- Solving right triangles and applications
Trig Functions of Any Angle
Extend trig functions beyond right triangles using reference angles, and master fundamental identities.
- Trig functions of any angle using reference angles
- Evaluating all six trig functions
- Reciprocal, quotient, and Pythagorean identities
- Even-odd properties and cofunction identities
Graphs of Trig Functions
Graph all six trig functions with transformations including amplitude, period, phase shift, and vertical shift.
- Graphing sine and cosine: amplitude and period
- Phase shift, vertical shift, and transformations
- Graphing tangent and cotangent
- Graphing secant and cosecant
Trigonometric Identities
Verify identities and master sum/difference, double-angle, half-angle, and product-to-sum formulas.
- Strategies for verifying trig identities
- Sum and difference formulas
- Double-angle and half-angle formulas
- Product-to-sum and sum-to-product formulas
Trigonometric Equations
Solve trig equations using algebraic techniques, identities, and inverse trig functions.
- Solving basic trig equations
- Solving equations using identities
- Equations involving multiple angles
- Inverse trig functions
Applications of Trigonometry
Apply the Law of Sines, Law of Cosines, triangle area formulas, and get introduced to vectors.
- The Law of Sines and the ambiguous case
- The Law of Cosines
- Area of triangles and Heron's formula
- Introduction to vectors
Polar Coordinates & Complex Numbers
Explore polar coordinates, convert between coordinate systems, graph polar equations, and use DeMoivre's Theorem.
- The polar coordinate system
- Converting between polar and rectangular
- Graphing polar equations
- Complex numbers in trig form and DeMoivre's Theorem
Ready to Get Started?
Begin with Module 1 to build a strong foundation in angle measurement. All materials are completely free!
Learning Tips
- Work through all lessons in order for best understanding
- Practice, practice, practice! Do all practice problems before the quiz
- Use the study guide to review before quizzes and exams
- Memorize the unit circle — it is the backbone of trigonometry
- Draw diagrams for every word problem involving triangles
- Use Desmos to visualize trig functions and their transformations