Teacher: Jim
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#### 1 Lesson 1 - Angles Measured in Radians or Degrees 20:33

Objectives: 1. Convert an angle between degrees and radians 2. Draw an angle in standard position

#### 2 Lesson 2 - Introducing Sine and Cosine 23:00

Objectives: 1. Find the exact value of sine and cosine given an angle 2. Find the exact value of sine and cosine given an angle passing through a point

#### 3 Lesson 3 - Sine and Cosine using the Unit Circle 07:34

Objectives: 1. Find the exact value of sine and cosine using a unit circle 2. Use the unit circle to find an angle that gives a specified trig ratio

#### 4 Lesson 4 - Inverse Sine and Cosine Functions 09:17

Objectives: 1. Find the exact value of an inverse sine or cosine function. 2. Simplify an expression with inverse sine or cosine. 3. Use a calculator to find an approximate value of an inverse sine or cosine function.

#### 5 Lesson 5 - Graphing Trigonometric Functions I 20:55

Connecting the Shape of Sine and Cosine to the Unit Circle

https://www.desmos.com/calculator/kxfekf0kgb

https://www.desmos.com/calculator/s8jg20tfws

#### 6 Lesson 6 - Graphing Trigonometric Functions II 23:19

Objectives: 1. Graph trigonometric functions 2. Identify phase shift/midline of a trigonometric function

#### 7 Lesson 7 - Modeling Trigonometric Functions 09:43

Objectives: 1. Model a trigonometric equation given periodic behavior

#### 8 Lesson 8 - Tangent and Cotangent Functions 11:50

Objectives: 1. Find the value of tangent and cotangent ratios given an angle 2. Find the value of tangent and cotangent ratios given other trig ratios

#### 9 Lesson 9 - Tangent and Slope 08:34

Objectives: 1. Find the slope of an angle 2. Find the angle of a line given a slope

#### 10 Lesson 10 - Secant and Cosecant Functions 08:23

Objectives: 1. Find the value of secant and cosecant ratios given an angle 2. Find the value of secant and cosecant ratios given other trig ratios

#### 11 Lesson 11 - Pythagorean Identity 13:05

Objectives: 1. Use the Pythagorean Identity to prove other identities 2. Use the Pythagorean Identity to find unknown trig ratios

#### 12 Lesson 12 - Addition Formulas for Sines and Cosines 15:13

Objectives: 1. Use addition formulas to find exact values for sine or cosine 2. Use addition formulas to simplify an expression as sine or cosine of a single angle

#### 13 Lesson 13 - Half-Angle and Double-Angle Formulas 21:30

Objectives: 1. Use a double-angle identity to find the exact value of expressions 2. Use a half-angle identity to find the exact value of expressions

#### 14 Lesson 14 - Proving other Trigonometric Identities 23:15

Objectives: 1. Prove trigonometric identities by manipulating one side 2. Prove trigonometric identities by manipulating both sides 3. Prove trigonometric identities using other identities/formulas

#### 15 Lesson 15 - Right Triangle Trigonometry 14:09

Objectives: 1. Identify trigonometric ratios of a right triangle 2. Solve for an unknown side length of a right triangle 3. Solve for an unknown angle of a right triangle

#### 16 Lesson 16 - Law of Sines and Law of Cosines 18:59

Objectives 1. Solve a triangle using Law of Sines 2. Solve a triangle using Law of Cosines

#### 17 Lesson 17 - Ambiguous Case for Law of Sines 15:49

Objectives 1. Identify and solve problems involving the Ambiguous Case for Law of Sines

#### 18 Lesson 18 - Determining the Area of a Triangle 09:43

Objectives 1. Find the area of a triangle given two sides and an included angle 2. Find the area of a triangle given three sides

#### 19 Lesson 19 - Applying Trigonometry 25:23

Objectives: 1. Apply trigonometric ratios to solve problems involving right triangles 2. Apply Law of Sines and Law of Cosines to solve problems involving non-right triangles

#### 19 Midterm Exam 01:17

This exam covers the first 19 lessons of the course. It is administered in two parts:

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed.This section should take no more than 60 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Addition Formulas for Sine and Cosine

Proving Trigonometric Identities

Tangent and Slope

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Determining the Area of a Triangle

#### 20 Lesson 20 - Polar Coordinates 21:41

Objectives: 1. Graph polar coordinates 2. Identify polar coordinates that coincide 3. Calculate the distance between two sets of polar coordinates

#### 21 Lesson 21 - Converting Points 14:28

Objectives: 1. Convert polar coordinates to rectangular coordinates 2. Convert rectangular coordinates to polar coordinates

#### 22 Lesson 22 - Vectors in Cartesian Coordinates I 19:54

Objectives: 1. Define vector between two points 2. Find the magnitude of a vector 3. Find the direction of a vector 4. Find a unit vector that goes in the same direction as a given vector

#### 23 Lesson 23 - Vectors in Cartesian Coordinates II 17:27

Objectives: 1. Apply addition, subtraction and scalar multiplication to vectors 2. Find the dot product between two vectors 3. Find the angle between two vectors

#### 24 Lesson 24 - Vectors in Polar Coordinates 08:11

Objectives: 1. Find the components of a vector given its magnitude and angle 2. Add two vectors given their magnitudes and angles

#### 25 Lesson 25 - Complex Numbers I 09:25

Ojectives: 1. Simplify the square root of negative numbers using the imaginary number i 2. Find the complex conjugate of a complex number 3. Graph a complex number in the complex plane 4. Find the magnitude of a complex number

#### 26 Lesson 26 - Complex Numbers II 15:40

Ojectives: 1. Find the magnitude of a complex number 2. Find the angle of a complex number 3. Write a complex number in trigonometric form

#### 27 Lesson 27 - Arithmetic of Complex Numbers 19:28

Objectives: 1. Add/subtract complex numbers 2. Multiply complex numbers 3. Divide complex numbers

#### 28 Lesson 28 - DeMoivre's Theorem 22:08

Objectives: 1. Multiply/divide two complex numbers using DeMoivre's Theorem 2. Find the powers of complex numbers using DeMoivre's Theorem 3. Find the roots of complex numbers using DeMoivre's Theorem

#### 29 Lesson 29 - Introduction to Linear Algebra and Matrices 07:35

Lesson Objectives: 1. Identify the order of a matrix 2. Write a vector using matrix form

#### 30 Lesson 30 - Row Operations of a Matrix 12:47

Objectives: 1. Apply row operations to a matrix

#### 31 Lesson 31 - Row Echelon and Reduced Row Echelon Form 27:25

Objectives: 1. Apply row operations to a matrix 2. Convert a matrix into Row Echelon Form 3. Convert a matrix into Reduced Row Echelon Form

#### 32 Lesson 32 - Coefficient Matrices 06:16

Objectives: 1. Represent a system of equations with a coefficient matrix

#### 33 Lesson 33 - Gaussian and Gauss-Jordan Elimination 24:20

Objectives: 1. Use Gaussian Elimination to solve a system of equations 2. Use Gauss-Jordan Elimination to solve a system of equations

#### 35 Lesson 35 - Matrix Multiplication 16:43

Objective: 1. Perform matrix multiplication

#### 36 Lesson 36 - Proofs by Mathematical Induction 16:53

Objectives: 1. Prove an identity involving sums using induction 2. Prove an identity involving divisibility using induction

#### 37 Lesson 37 - Zeros and Factors of Polynomials 06:47

Objectives: 1. Identify the zeros of a polynomial 2. Use Factor Theorem to determine if a binomial is a factor of a polynomial

#### 38 Lesson 38 - Rational Root Theorem 16:38

Objectives: 1. Find the possible rational zeros of a polynomial 2. Find actual rational zeros of a polynomial

#### 39 Lesson 39 - Synthetic Division 17:50

Objectives: 1. Apply Synthetic Division to a polynomial 2. Use Synthetic Division to find all the zeros of a polynomial

#### 40 Lesson 40 - Repeated Zeros of a Polynomial 16:41

Objectives: 1. State the polynomial function given repeated zeros 2. Find the zeros of a polynomial with repeated zeros

#### 41 Lesson 41 - Fundamental Theorem of Algebra 22:31

Objectives: 1. Identify the number of zeros of a polynomial 2. State a polynomial given the zeros it has 3. Find all the zeros of a polynomial

#### 41 Final Exam 01:25

This exam covers the entire 41 lessons of the course, focusing on the lessons 20-41.

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed. This section should take no more than 75 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Unit Vectors

Operations with Vectors and Matrices

Arithmetic with Complex Numbers

DeMoivre's Theorem

Row Echelon and Reduced Row Echelon Form of Matrices

Gaussian and Gauss-Jordan Elimination

Factors and Zeros of Polynomials

Finding Zeros of Polynomials using Synthetic Division, Rational Root Theorem, Repeated Zeros and Fundamental Theorem of Algebra.

Course Description

Pre-calculus weaves together previous study of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers. Particular emphasis is placed on students' ability to reason critically on their own without the use of technology. The tests are broken into two parts: Part 1 covers problems that can be solved without technology and Part 2 covers problems that can be solved with technology.

Course Goals

Upon completion of this course, students will be prepared to move on to Calculus. Students will be able to apply trigonometry, vectors, polynomials and matrices to a variety of situations.

Course Requirements

Student taking this course are expected to have mastered the most important topics taught in an Algebra 2 course. Important topics to master are:

Factoring

Plotting points and graphs in the Cartesian Plane

Target Audience

This video course is primarily intended for students who have already mastered Algebra 2 concepts(typically 16+) and are planning on taking Calculus or for students in Precalculus or Calculus and need to review previously taught concepts (typically 17+).

Technology

The majority of the lessons are taught so that technology is not needed. However there are some where the use of a calculator or computer is required. Under the Additional Resources for Parents are tutorial videos that show how to use either online resources or a calculator to perform the work needed. The free online resources used are www.wolframalpha.com and www.desmos.com. The calculator used is the TI-83 which is the most commonly used graphing calcuculator in schools. If you use any TI calculator with the number 83 or 84, the instructions will be fine.

Course Includes

• 18 hours of video
• 41 video lessons
• 41 skill worksheets
• 41 worksheet review videos
• 41 online lesson quizzes
• 2 tests (Additional Resources for Parents)
• Blank Lesson Notes Sheets for all lessons
• Completed Lesson Notes (Additional Resources for Parents)
• Completed Worksheet Problems (Additional Resources for Parents)

Course Topics

• Angles Measured in Radians or Degrees
• Introducing Sine and Cosine
• Sine and Cosine using the Unit Circle
• Inverse Sine and Cosine Functions
• Graphing Trigonometric Functions I
• Graphing Trigonometric Functions II
• Modeling Trigonometric Functions
• Tangent and Cotangent Functions
• Tangent and Slope
• Secant and Cosecant Functions
• Pythagorean Identity
• Addition Formulas for Sines and Cosines
• Half Angle and Double Angle Formulas
• Proving other Trigonometric Identities
• Right Triangle Trigonometry
• Law of Sines and Law of Cosines
• Ambiguous Case for Law of Sines
• Determining the Area of a Triangle
• Applying Trigonometry
• Polar Coordinates
• Converting Points
• Vectors in Cartesian Coordinates I
• Vectors in Cartesian Coordinates II
• Vectors in Polar Coordinates
• Complex Numbers I
• Complex Numbers II
• Arithmetic of Complex Numbers
• DeMoivre's Theorem
• Introduction to Linear Algebra and Matrices
• Row Operations of a Matrix
• Row Echelon and Reduced Row Echelon Form
• Coefficient Matrices
• Gaussian and GaussJordan Elimination
• Addition on Matrices and Vectors
• Matrix Multiplication
• Proofs by Mathematical Induction
• Zeros and Factors of Polynomials
• Rational Root Theorem
• Synthetic Division
• Repeated Zeros of a Polynomial
• Fundamental Theorem of Algebra
•
• Teacher: Jim
• Areas of expertise: Mathematics, Spanish, Technology
• Education: Augustana College St. Ambrose University
• Interests: Board Gaming
• Skills: Singing
• Associations: National Council of Teachers of Mathematics, Illinois Council of Teachers of Mathematics

I want to make the world a better place by helping those around me reach their full potential. If we all do our best to help everyone do their best, the world would be a much better place.

#### Lesson 1 - Angles Measured in Radians or Degrees

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 2 - Introducing Sine and Cosine

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 2 - Introducing Sine and Cosine - Calculator Supplement

This video shows how to use the calculator for Introducing Sine and Cosine

#### Lesson 2 - Introducing Sine and Cosine - Computer Supplement

This video shows how to use the computer for Introducing Sine and Cosine

#### Lesson 3 - Sine and Cosine using the Unit Circle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 4 - Inverse Sine and Cosine Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 4 - Inverse Sine and Cosine Function - Calculator

This video shows how to use the calculator for Inverse Sine and Cosine Functions

#### Lesson 4 - Inverse Sine and Cosine Function - Computer

This video shows how to use the computer for Inverse Sine and Cosine Functions

#### Lesson 5 - Graphing Trigonometric Functions I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 5 - Graphing Trigonometric Functions I - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions I

#### Lesson 5 - Graphing Trigonometric Functions I - Computer

This video shows how to use the computer for Graphing Trigonometric Functions I

#### Lesson 6 - Graphing Trigonometric Functions II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 6 - Graphing Trigonometric Functions II - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions II

#### Lesson 6 - Graphing Trigonometric Functions II - Computer

This video shows how to use the computer for Graphing Trigonometric Functions II

#### Lesson 7 - Modeling Trigonometric Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 8 - Tangent and Cotangent Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 9 - Tangent and Slope

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 10 - Secant and Cosecant Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 11 - Pythagorean Identity

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 12 - Addition Formulas for Sines and Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 13 - Half-Angle and Double-Angle Formulas

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 14 - Proving other Trigonometric Identities

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 15 - Right Triangle Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 16 - Law of Sines and Law of Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 17 - Ambiguous Case for Law of Sines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 18 - Determining the Area of a Triangle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 19 - Applying Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Midterm Exam

This exam covers the first 19 lessons of the course. It is administered in two parts:

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed.This section should take no more than 60 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Addition Formulas for Sine and Cosine

Proving Trigonometric Identities

Tangent and Slope

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Determining the Area of a Triangle

#### Lesson 20 - Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 21 - Converting Points

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 22 - Vectors in Cartesian Coordinates I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 23 - Vectors in Cartesian Coordinates II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 24 - Vectors in Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 25 - Complex Numbers I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 26 - Complex Numbers II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 27 - Arithmetic of Complex Numbers

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 28 - DeMoivre's Theorem

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 29 - Introduction to Linear Algebra and Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 30 - Row Operations of a Matrix

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 31 - Row Echelon and Reduced Row Echelon Form

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 31 - Row Echelon and Reduced Row Echelon Form - Calculator

This video shows how to use the calculator for Row Echelon and Reduced Row Echelon Form

#### Lesson 31 - Row Echelon and Reduced Row Echelon Form - Computer

This video shows how to use the computer for Row Echelon and Row Echelon Form

#### Lesson 32 - Coefficient Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Final Exam

This exam covers the entire 41 lessons of the course, focusing on the lessons 20-41.

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed. This section should take no more than 75 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.

Topics to focus on:

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Unit Vectors

Operations with Vectors and Matrices

Arithmetic with Complex Numbers

DeMoivre's Theorem

Row Echelon and Reduced Row Echelon Form of Matrices

Gaussian and Gauss-Jordan Elimination

Factors and Zeros of Polynomials

Finding Zeros of Polynomials using Synthetic Division, Rational Root Theorem, Repeated Zeros and Fundamental Theorem of Algebra.

#### Lesson 33 - Gaussian and Gauss-Jordan Elimination

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 34 - Addition on Matrices and Vectors

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 35 - Matrix Multiplication

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 36 - Proofs by Mathematical Induction

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 37 - Zeros and Factors of Polynomials

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 38 - Rational Root Theorem

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 39 - Synthetic Division

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 40 - Repeated Zeros of a Polynomial

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

#### Lesson 41 - Fundamental Theorem of Algebra

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems