Trigonometry· Study notes
Shape and Angle
The six trigonometric functions from the right triangle to the unit circle, their graphs, identities and equations, then the laws of sines and cosines, vectors, polar coordinates and complex numbers.
What you'll be able to do
- Evaluate trig functions exactly at special angles
- Graph sinusoids and their transformations
- Verify identities and solve trig equations
- Solve any triangle
Read the notes as a guided lesson
Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics
Vectors and the Dot Product
8 lessonsComponents, magnitude & direction, the dot product, projection, and applications
Polar Coordinates and Complex Numbers
8 lessonsPlotting, conversions, polar graphs, trig form, products, and DeMoivre's Theorem
Angles and Their Measure
9 lessonsStandard position, radians, arc length, sector area, and speed
Right Triangle Trigonometry
7 lessonsThe six ratios, special angles, solving triangles, cofunctions, and applications
The Unit Circle and Circular Functions
8 lessonsSpecial angles, reference angles, signs, periodicity, even/odd, and terminal points
Graphs of Sine and Cosine
8 lessonsAmplitude, period, phase shift, vertical shift, and modeling
Graphs of the Other Trigonometric Functions
6 lessonsTangent, cotangent, secant, and cosecant: periods, asymptotes, and transformations
Inverse Trigonometric Functions
8 lessonsDefinitions, exact values, compositions, graphs & equations
Trigonometric Identities
7 lessonsFundamental identities, simplifying, and verifying
Sum, Difference, and Multiple-Angle Formulas
9 lessonsExact values, double & half-angles, power-reducing, product-to-sum
Trigonometric Equations
8 lessonsBasic equations, factoring, quadratic form, identities, multiple angles, and inverses