Trigonometry Objectives

We list below the topics covered in Trigonometry in Math 225 and Math 226. Items marked in GREEN are to be covered in Math 225 as they occur in the course of teaching the material on limits and derivatives. Items marked in BLUE are to be covered in Math 226 as they deal with inverse trigonometric functions. Items marked in RED can be omitted at the instructors discretion.

Measurement of Angles, Arcs, and Sectors
- Using Radians, Degrees, or Grads to Measure Angles
- Length of an Arc and Area of a Sector of a Circle
- Circular Motion
The Trigonometric Functions
- Definition of the Six Trigonometric Functions
- Values of the Trigonometric Functions at some multiples of 15 degrees.
- Trigonometric Functions for right triangles
- Solving Right Triangles
- Applications of Right Triangle Trigonometry
- Circular Functions
Graphs of Trigonometric Functions
- Graphing Generic Sine and Cosine Functions
- Shifting Generic Curves Right/Left or Up/Down
- Using the Graphing Calculator to Graph Functions by Addition of Ordinates
- Graphing the Tangent and Cotangent Functions
- Graphing the Secant and Cosecant Functions
- Qualitative Analysis of Trigonometric Functions
Inverse Trigonometic Functions
- Relations, Functions, and Their Inverses
- Inverses of Trigometric Functions
- Finding Inverses of Trigonometric Functions Using a Calculator
Basic Trigonometric Identities
- Fundamental Identities
- Opposite Angle Identities
- Additional Techniques to Prove Identities
Sum and Difference Identities
- Sum and Difference Identities for Cosine
- Some Identities Useful in Calculus
- Sum and Difference Identity for Tangent
- Identities Involving Sums and Differences of Pi and Pi/2.
Additional Identities
- Double Angle Identities
- Half Angle Identities
- Identities to Rewrite Sums and Products
Trigonometric Equations
- Solving Basic Trigonometric Equations
- Solving Trigonometric Equations Involving Factoring
- Solving Trigonometric Equations Where the Argument is a Function
- Using Identities to Solve Trigonometric Equations
Law of Sines and Law of Cosines
- Derivation of the Law of Sines
- The Ambiguous Case
- Applications of the Law of Sines
- Derivation of the Law of Cosines
- Applications of the Law of Cosines
- Area of a Triangle
Vectors
- Addition of Vectors
- Geometric Resolution of Vectors
- Algebraic Resolution of Vectors
- Work, Inclined Planes, and the Dot Product
Complex Numbers
- Algebraic Operations with Complex Numbers
- Trigonometric and Polar Representation of Complex Numbers
- DeMoivre's Formula
Polar Coordinates
- The Polar Coordinate System
- Parametric Equations
- Other Graphs in Polar Coordinates