II. Transformation
II. Transformation
II.1.1. Abstract Translations of the Plane
II.1.2. Vectors and the Method of Coordinates on a Plane
II.1.3. Translating Sets and Graphs
II.2.1. Scaling Vectors
II.2.2. Circles and the Polar Form of a Vector
II.2.3. Scaling Subsets of the Plane
II.3.1. Units
II.3.2. Linear Scaling
II.3.3. Simple Nonlinear Scaling
II.3.4. General Nonlinear Scaling
II.4.1. Absolute and Relative Movement
II.4.2. Parameterized Lines
II.5.1. Orthogonality of Vectors and Lines
II.5.2. Distance from Points to Lines
II.5.3. Reflecting Sets across Lines
II.6.1. Reflection and Inverse Functions
II.6.2. Restricting Domain to Guarantee Invertibility
II.7.1. Abstract Motions on a Circle
II.7.2. Circle Actions and the Method of Coordinates on a Circle
II.7.3. Rotating Points around a Point
II.8.1. Fractions of a Circle and Measurement of Angles
II.8.2. The Sine, Cosine, and Tangent Functions
II.8.3. Angle Addition Formulae for Trigonometric Functions
II.8.4. Parameterizing Rotational Motion
II.8.5. Basic Surveying Problems
II.9.1. Reflections and Rotation by Half of a Circle
II.9.2. Inverting the Axes
Worksheet II.1: Translation and the Addition of Real Numbers
Worksheet II.2: Translating and Scaling Subsets of the Plane
Worksheet II.3: Units and Scaling
Worksheet II.4: Parameterization of Linear Motion
Worksheet II.5: Orthogonality and Reflection
Worksheet II.6: Inverting Functions and their Restrictions
Worksheet II.7: Arithmetic on Circles
Worksheet II.8A: Approximating Points on the Unit Circle
Worksheet II.8B: Parameterized Rotational Motion
Worksheet II.9: Reciprocals of Polynomials