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

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

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

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.

Additional Resources:

Connecting the Shape of Sine and Cosine to the Unit Circle

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

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

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

Objectives:
1. Model a trigonometric equation given periodic behavior

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

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

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

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

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

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

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

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

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

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

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

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

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:**

Angles in Radians and Degrees

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

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

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

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

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

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

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

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

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

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

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

Objectives:
1. Apply row operations to a matrix

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

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

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

Objectives:
1. Perform addition involving matrices
2. Perform addition involving vectors

Objective:
1. Perform matrix multiplication

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

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

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

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

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

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

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

Solving Linear/Quadratic Equations

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)
- Answer keys to all 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
- Issues I care about:

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:**

Angles in Radians and Degrees

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

**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.

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

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

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

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

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

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

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

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

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