# Chapter 8: Further Applications of Trigonometry

Chapter 8 reading

**Section 8.1 Videos**

Video Lessons

- The Law of Sines: The basics
- The Law of Sines: The ambiguous case
- The Law of Cosines
- The Law of Cosines: Applications
- The Area of a Triangle Using Heron’s Formula

Video Examples

- The Law of Sines: Applications I
- The Law of Sines: Applications 2
- Example: Solve a Triangle Using the Law of Sines (given two sides and an angle)
- Example: Solve a Triangle Using the Law of Sines (given two angles and one side)
- Example 1: Determine an Unknown Length Using the Law of Sines
- Example 2: Determine an Unknown Length Using the Law of Sines
- Example 3: Determine an Unknown Length Using the Law of Sine (airplane problem)
- Example 1: Application of the Law of Cosines (width of lake)
- Example 2: Application of the Law of Cosines (distance plane travels)
- Example 3: Application of the Law of Cosines (diagonal of parallelogram)
- Example 4: Application of the Law of Cosines (measure of an angle)

**Section 8.2 Videos**

Video Lessons

- Polar Coordinates
- Animation: Rectangular and Polar Coordinates
- Graph Polar Equations I
- Graph Polar Equations II
- Animation: Graph Polar Equations
- Graphing Polar Equations on the TI84 Graphing Calculator

Video Examples

- Example: Identify 4 Possible Polar Coordinates for a Point Using Degrees
- Example: Identify 4 Possible Polar Coordinates for a Point Using Radians
- Example: Convert a Point in Rectangular Coordinates to Polar Coordinates Using Degrees
- Example: Convert a Point in Rectangular Coordinates to Polar Coordinates Using Radians
- Example: Convert a Point in Polar Coordinates to Rectangular Coordinates
- Ex: Find the Polar Equation of a Circle With Center at the Origin
- Ex: Find the Polar Equation for a Horizontal Line
- Ex: Find the Polar Equation for a Line
- Ex: Find the Polar Equation for a Parabola
- Ex: Find the Rectangular Equation of a Circle from a Polar Equation
- Ex: Convert a Rectangular Equation to a Polar Equation

**Section 8.3 Videos**

Video Lessons

- Complex Numbers
- Complex Number Operations
- Complex Number Operations on the TI-84
- Trigonometric Form of Complex Numbers
- Product and Quotient of Complex Numbers in Trig Form
- DeMoivre’s Theorm: Powers of Complex Numbers in Trig Form
- Roots of Complex Numbers

Video Examples

- Ex: Determine a Real, Imaginary, and Complex Number
- Ex : Simplify Imaginary and Complex Numbers
- Ex: Simplify, Add, and Subtract Imaginary and Complex Numbers
- Ex 1: Adding and Subtracting Complex Numbers
- Ex 2: Adding and Subtracting Complex Numbers
- Ex 1: Simplify and Multiply Complex Numbers
- Ex 2: Multiply Complex Numbers
- Ex 3: Multiply Complex Numbers
- Ex: Multiplying Complex Conjugates
- Ex: Raising the imaginary unit i to powers
- Ex: Dividing Complex Numbers
- Ex: Convert a Complex Number in Cartesian Form to Exponential Form
- Ex: Convert a Complex Number in Exponential Form to Cartesian Form
- Ex: Raise a Complex Number in Polar Form to a Power - Demoivre's Theorem
- Ex: Raise a Complex Number in Polar Form to a Power Using Exponential Form
- Ex 1: Raise a Complex Number in Cartesian Form to a Power - Demoivre's Theorem
- Ex 2: Raise a Complex Number in Cartesian Form to a Power - Demoivre's Theorem

**Section 8.4 Videos**

Video Lessons

- Introduction to Vectors
- Vector Operations
- Find the Component Form of a Vector Given Magnitude and Direction

Video Examples

(note: this section is not in the currently-available printed text)

**Section 8.4.5 Videos**

Video Lessons

- Dot Product and angle between vectors
- Projection (first 6 minutes)
- Force and Work

**Section 8.5 Videos**

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