Trigonometry

1. Angles Measured in Degrees

2. Angles Measured in Radians

3. Common Radian Measurements

4. Radian Measures Not in Terms of Pi

5. Coterminal Angles

6. Converting Between Radians and Degrees

1. Arc Lengths and Angles with the Unit Circle

2. Cutting the Unit Circle into Common Angles or Arc Lengths

3. Terminal Points on the Unit Circle

4. Determining if a Point is on The Unit Circle

1. Circular Motion: Angular Speed

2. Circular Motion: Linear Speed

1. The Pythagorean Theorem

2. Special Right Triangles: 30-60-90 and 45-45-90

3. Reference Triangles and Reference Angles

4. Trigonometric Functions of Acute Angles - SOH CAH TOA

5. Using Trigonometry to Find a Side of a Right Triangle

6. Using Inverse Trig Functions to Solve for an Angle in a Right Triangle

7. Trigonometric Functions of Any Angle

8. The Signs of The Trigonometric Functions

9. Finding the Value of Any Trig. Function Given the Value of One

1. Inverse Trigonometric Functions

2. Inverse Sine

3. Inverse Cosine

4. Inverse Tangent

5. Composition of Trig and Inverse Trig Functions

1. The Area of a Triangle

2. Finding the Area of a Triangle, Given Two Sides and the Included Angle

1. Basic Properties of Triangles

Law of Sines

1. The Law of Sines

2. The Difficulty with Using Sine Inverse when Solving a Triangle

3. Using Law of Sines to Solve a Triangle with "No Solution"

4. Using Law of Sines to Solve a Triangle with One Solution

5. Using Law of Sines to Solve a Triangle with Two Solutions

Law of Cosines

1. The Law of Cosines

2. Using the Law of Cosines to Solve for a Side of a Triangle

3. Using the Law of Cosines to Solve for an Angle

4. Navigation: Basics of Bearings

5. Application Using Law of Cosines & Bearings

1. What are Even and Odd Functions?

2. Even and Odd Trigonometric Functions

3. Summary of Even and Odd Trig Functions

1. The Sine Parent Function

2. The Cosine Parent Function

3. Graphing a Transformed Sine Function

4. Graphing a Transformed Cosine Function

5. Secant and Cosecant Parent Function Graphs

6. Graphing Two Cycles of a Transformed Cosecant Function

7. Graphing Two Cycles of a Transformed Secant Function

8. Tangent and Cotangent Parent Function Graphs

9. Graphing Two Cycles of a Transformed Tangent Function

10. Graphing Two Cycles of a Transformed Cotangent Function

1. Simple Harmonic Motion Examples

2. Using a Simple Harmonic Motion Model

3. Example: Determining the function for a pendulum exhibiting simple harmonic motion

Writing Trigonometric Functions in Terms of Sine and Cosine

1. Writing Trig Functions in Terms of Sine and Cosine

2. Simplifying Expressions & Proving Trig Identities Using Sine & Cosine

The Pythagorean Identities

1. The Pythagorean Identities and Their Alternate Forms

2. Using a Pythagorean Identity to Algebraically Write One Trig. Function in Terms of Another

3. Simplifying Trig Expressions and Doing Proofs Using the Pythagorean Identities

Proving Trigonometric Identities

1. Proving or Disproving an Identity

2. Basic Strategies for Proving Trigonometric Identities

3. Proving Trig Identities Involving Fractions

4. Proving Trig Identities Involving Conjugates

5. Proving Trig Identities Involving Complex Fractions

Addition and Subtraction Formulas

1. A Trigonometric Function of a Sum or Difference

2. Some Ways to Use the Addition and Subtraction Formulas

3. A Proof Using Addition & Subtraction Formulas

Double-Angle Formulas

1. Deriving the Double-Angle Formulas from the Addition Formulas

2. Basic Examples Using the Double-Angle Formulas

3. A Proof Using Double-Angle Formulas (and other techniques)

Power-Lowering Formulas

1. Deriving Power-Lowering Formulas

2. Example Using Power-Lowering Formula

Half-Angle Formulas

1. Deriving Half-Angle Formulas

2. Examples Using Half-Angle Formulas

1. Introduction to Solving Trig Equations Using Inverse Trig Functions

2. Examples: Solving Trig Equations Using Inverse Trig Functions

3. Solving Higher-Degree Trigonometric Equations

4. Solving Trig Equations Using Identities

5. Solving Trigonometric Equations By Factoring

6. Solving Trigonometric Equations with a Multiple Angle

1. Polar and Rectangular Coordinate Systems

2. Plotting Polar Coordinates

3. Converting Rectangular Coordinates to Polar Coordinates

4. Converting Polar Coordinates to Rectangular Coordinates

5. Converting an Equation from Rectangular Form to Polar Form

6. Converting an Equation from Polar Form to Rectangular Form

7. Graphing Basic Polar Equations

8. Graphing Polar Equations Using Patterns and Symmetry

9. Graphing Polar Equations Using the Corresponding Rectangular Coordinate System Graph

1. Complex Numbers in Rectangular Form and Graphing

2. The Modulus of a Complex Number

3. The Argument of a Complex Number

4. Writing a Complex Number in Polar Form

5. Multiplying Complex Numbers in Polar Form

6. Raising Polar Complex Numbers to a Power (DeMoivre's Theorem)

7. Dividing Complex Numbers in Polar Form

8. Roots of Complex Numbers in Polar Form

9. Examples: Roots of Complex Numbers in Polar Form

Two-Dimensional Vectors

1. Introduction to Vectors

2. Ways to Represent Vectors

3. Unit Vectors

4. Magnitude of a 2D Vector

5. Direction of a 2D Vector

6. Scalar Multiplication with 2D Vectors

7. Addition and Subtraction of 2D Vectors

8. Dot Product

9. Calculating the Angle Between Vectors

10. Force Vectors

11. An Application of Vectors: True Velocity

12. Example: True Velocity Vector

13. Understanding Vector Projections

14. Finding a Unit Vector in the Same Direction as a Given Vector

15. Calculating the Magnitude of a Projection Vector

16. The Strategy for Calculating a Projection Vector

Three-Dimensional Vectors

1. Three Dimensional Coordinate System

2. Vectors in Three Dimensions

3. Magnitude of a 3D Vector

4. Arithmetic of 3D Vectors

5. The Dot Product and Angle Between 3d Vectors

6. Direction Angles of 3D Vectors

7. The Concept of Vector Cross Product

8. Calculating a Cross Product Vector