**Expository Pages:**

- The Definition(s) of Trigonometry: the unit circle, standard position ratios, and triangle ratios
- Generating the Sine Function: (GIF animation): see the sine function developed from the unit circle
- Basic Trigonometric Values: multiples of 30 and 45 degrees
- Multiples of 15 Degrees: derivations of trig values for 15 and 75 degrees
- Multiples of 18 Degrees: derivations of trig values for 18, 36, 54, and 72 degrees
- Trigonometric Graphs: the six basic graphs understood as projections
- The Trig Functions and the Unit Circle (GIF animation): see the 6 trig functions vary through the first quadrant of the unit circle
- Basic Trigonometric Identities: reciprocal, ratio, Pythagorean, symmetric, and cofunction identities
- Angle Sum and Difference Identities: angle sum, angle difference, double angle, power-reducing, half-angle, product-to-sum, and sum-to-product formulas
- Triangle Identities: Law of Sines, Law of Cosines, Law of Tangents, and a product-sum identity
- Definitions and Graphs of the Inverse Trig Functions: the six inverse trig functions (some with two forms)
- Basic Inverse Trig Function Identities: reciprocal, symmetric, and cofunction identities
- Compositions of Trig and Inverse Trig
Functions: 108 compositions with 74 graphs
- Eccentricity of a Conic (GIF animation): see the conic graph change as its eccentricity varies
- Taylor Polynomials (GIF animation): see the Taylor polynomials converge to the sine function
- Imaginary Numbers and Trigonometry: understanding non-real numbers using trig
- Functions of Complex Numbers: defining trig and inverse trig functions for non-real values

**Interactive Pages:**

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- Trig
Values and the Unit Circle (web
*Mathematica*): vary the parameter to see the functions as projections - Exploring the Graph of the Sine Function (
*Excel*): vary the coefficients of the sine function and watch the graph change - Exploring the Graph of the Cosine Function
(
*Excel*): vary the coefficients of the sine function and watch the graph change - Exploring the Graph of the Tangent Function
(
*Excel*): vary the coefficients of the sine function and watch the graph change - Exploring the Graph of the Cotangent
Function (
*Excel*): vary the coefficients of the sine function and watch the graph change - Exploring the Graph of the Secant Function
(
*Excel*): vary the coefficients of the sine function and watch the graph change - Exploring the Graph of the Cosecant
Function (
*Excel*): vary the coefficients of the sine function and watch the graph change - Curvilinear Coordinates and the Sine Function
(
*Excel*): vary the coefficients of the sine function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates - Curvilinear Coordinates and the Tangent
Function (
*Excel*): vary the coefficients of the tangent function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates - Curvilinear Coordinates and the Secant
Function (
*Excel*): vary the coefficients of the secant function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates - Curvilinear Coordinates and the Inverse
Sine Function (
*Excel*): vary the coefficients of the inverse sine function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates - Curvilinear Coordinates and the Inverse
Tangent Function (
*Excel*): vary the coefficients of the inverse tangent function and watch the graph in rectangular, polar, parabolic, elliptic, or bipolar coordinates - Rose
Analyzer (web
*Mathematica*): vary the parameters in the polar equation of the rose - Limacon
Analyzer (web
*Mathematica*): vary the parameters in the polar equation of the limacon - Lissajous
Curve Analyzer (web
*Mathematica*): vary the parameters in the parametric equations of family of curves of Lissajous - 2D
Matrix Transformations (web
*Mathematica*): input a matrix and see it iteratively transform a simple geometric object - 2D
Homogeneous Transformations (web
*Mathematica*): input a matrix and see it iteratively transform a simple geometric object represented with homogeneous coordinates - Exploring
Fourier Series (web
*Mathematica*): vary the generic Fourier series term, and see the effect on the graph - Complex
Sine Function (web
*Mathematica*): vary the parameters in the complex sine function, and view subsets of the 4D graph - Complex
Arcsine Function (web
*Mathematica*): vary the parameters in the complex arcsine function, and view subsets of the 4D graph - Complex
Exponential Function (web
*Mathematica*): vary the parameters in the complex exponential function, and view subsets of the 4D graph (especially the imaginary parts)

- Standard
Position Trig Ratios Drillmaster (web
*Mathematica*): practice the 6 basic trig ratios from an angle in standard position - Right
Triangle Trig Ratios Drillmaster (web
*Mathematica*): practice the 6 basic trig ratios from a right triangle - Converting
Radians to Degrees Drillmaster (web
*Mathematica*): practice converting special angles to degrees - Converting
Degrees to Radians Drillmaster (web
*Mathematica*): practice converting special angles to radians - Special
Angle Sine and Cosine Values Drillmaster (web
*Mathematica*): practice the sine and cosine ratios for the special angles, in both degrees and radians - Special
Angle Trig Values Drillmaster (web
*Mathematica*): practice the 6 basic trig ratios for the special angles, in both degrees and radians - Sine
Graph Characteristics Drillmaster (web
*Mathematica*): practice identifying amplitude, period, and vertical translation from a graph