Trigonometric functions
Sine and cosine functions developed from unit circle
The remaining four trigonometric functions
Angles and trigonometric functions of angles
Radian measure and circular motion
Graphs of trigonometric functions
Inverse trigonometric functions
Trigonometric identities for a single angle
Identities for sums and differences, multiple angle identities
Product identities
Conditional equations
Harmonic motion (optional)
Applications of trigonometry
Right triangles
Oblique triangles
Polar coordinates
Polar form of complex numbers
Demoivre’s theorem
Matrices and Vectors
Vectors and vector operations
Matrices and matrix operations
Applications to linear systems
Logic and Proof
Sets and set operations
Disjunction, conjunction, negation, implication and equivalence
Direct and indirect proofs
Binomial theorem
Induction
Parametric Equations
Sketching parametric curves, including orientation
Parameterizing curves