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The Unit Circle is a concept that is used eminsely in trigonometry and into calculus. This video coveres the basics of the Unit Circle (degrees, radians, and coordinates) such that students understand where each of the values come from.

Converting between radian and degree measurements.

Answers to practice worksheet.

Finding sine and cosine ratios in right triangles and using the unit circle.

Answers to practice worksheet.

Using the restricted parameters of the inverse functions to simplify/evaluate expressions.

Answers to practice worksheet.

Use the information learned in the previous lesson and in the unit circle lesson to graph the sine and cosine functions.

Answers to practice worksheet.

Model different situations using trigonometric functions.

Answers to practice worksheet.

Finding tangent and cotangent ratios using the unit circle, how they are each related to sine and cosine, and finding their ratios given other trig ratios.

Answers to practice worksheet.

Finding their relationships with sine and cosine, finding the ratios on the unit circle, calculating their ratios given other trig ratios.

Answers to practice worksheet.

Finding the slope of an angle give side lengths, and find the angle of a line given the slope.

Answers to practice worksheet.

Unit Circle Test

We will discuss what the pythagorean theorem that relates sine to cosine is and how the other pythaogrean identities are related to it. Then, we will find trig ratios using the identities.

Answers to practice worksheet.

Finding exact values of trig functions for angles not on the unit circle. Simplifying expressions into one trig function.

Answers to practice worksheet.

Use the half and double angle formulas to find exact values for trig functions.

Answers to practice worksheet.

Solving trig equations.

Answers to practice worksheet.

Analytical Trig Test

Identify the trig ratios of a right triangle, solve for unknown side lengths, find unknown angle measures, and solve a right triangle.

Answers to practice worksheet.

Using the Law of Sines with non-right triangles to find side lengths and angle measures.

Answers to practice worksheet.

Using the law of cosines with non-right triangles to find side lengths and angle measures.

Answers to practice worksheet.

Finding the area of a triangle if given two sides and the included angle or if given all three sides of the triangle.

Answers to practice worksheet.

Applying trigonometry to real world situations.

Answers to practice worksheet.

Triangular Trigonometry Test

Graphing polar coordinates, identifying polar coordinates with more than one way, and calculating the distance between polar coordinates.

Answers to practice worksheet.

Convert between polar to rectangular and rectangular to polar coordinates.

Answers to practice worksheet.

Define vectors between two points, find the magnitude of a vectors, find the directional angle of a vector, and find a unit vector

Answers to practice worksheet.

Using addition, subtraction, scalar multiplication, and the dot product with vectors. Find the angle between two vectors.

Answers to practice worksheet.

Find components of vectors given its magnitude and angle and add two vectors given their magnitude and angles.

Answers to practice worksheet.

Simplifying square roots of negative numbers, simplify expression with i, finding complex conjugates, and graphing complex numbers

Answers to practice worksheet.

Finding the magnitude of a complex number, finding the angle of a complex number, and writing a complex number in trigonometric form

Answers to practice worksheet.

Multiply and divide complex numbers, find powers of complex number, and find roots of complex numbers

Answers to practice worksheet.

Polar Coordinates, Vectors, and Complex Numbers Test

Proving statements using mathematical induction.

Answers to practice worksheet.

The Fundamental Theorem of Algebra

Answers to practice worksheet.

Identify the order (dimensions of a matrix and identify the entries of a matrix.

Answers to practice worksheet.

Manipulate matrices using row operations

Answers to practice worksheet.

Use row operations in order to put matrices into row echelon and reduced row echelon forms.

Answers to practice worksheet.

Representing a system of equations with matrices

Answers to practice worksheet.

Using the Guassian and Guass-Jordan elimination methods in order to solve a system of equations.

Answers to practice worksheet.

Adding, subtracting, and multiplying matrices.

Answers to practice worksheet.

Proofs, Fund Theorem, Linear Algebra Test.

**Course Description: **

This Precalculus video course puts together the many concepts taught in Algebra 1, Geometry, and Algebra 2 in order to prepare students for Calculus and other subsequent math courses. In general, this course covers unit circle trigonometry, analytical trigonometry, right triangle trigonometry, the polar coordinate system, vectors, complex numbers, proofs by mathematical induction, the fundamental theorem of algebra, and an introduction to linear algebra. In each of the lessons, students are exposed to the basics skills of the concepts and challenged to use and improve their critical thinking skills.

**The course includes:**

12+ hours of video

5 units

34 instructional videos

34 blank pdf notes for students to use and fill in while watching the instructional videos

34 practice worksheets for students to practice and master the concepts being taught

34 answers key and videos (I explain step by step how to arrive at the correct answer)

350+ practice problems and step by step resolutions

5 tests (1 at the end of each unit)

5 test answer keys (one for each unit test)

**Course Goals: **Upon completion of this course, students will be well prepared for Calculus and have an introduction to a Linear Algebra course. Students will have a solid foundation on trigonometry, vectors, and matrices. Students will not only be able to use these skills to solve problems, but they will also be able to apply them to different situations.

**Target Audience: **This course is for students who have mastered the concepts taught in a traditional Algebra 2 course and are planning to take Calculus, or for those currently enrolled in a Precalculus class but need additional practice with the concepts being taught.

**Technology:** Although the course is taught such that a calculator is not necessary, a student may be more comfortable using one. If a student chooses to use a calculator make sure it has trigonometric functionality (a basic scientific calculator would not suffice).

**Course Concepts:**

**Unit 1 – Unit Circle Trigonometry **

The Unit Circle

Angle Measures in both radians and degrees

Sine and Cosine Ratios

Inverse Sine and Cosine

Graphing Sine and Cosine

Modeling real world situations with trigonometric functions

Tangent and Cotangent Ratios

Secant and Cosecant Ratios

Tangent and Slope

**Unit 2 – Analytical Trigonometry**

Pythagorean Identities

Addition and Subtraction Formulas

Half and Double Angle Formulas

Solving trig equations

**Unit 3 – Triangular Trigonometry**

Right Triangular Trig

Law of Sines

Law of Cosines

Area of a Triangle

Applying trig to real world situations

**Unit 4 – Polar Coordinates, Vectors, and Complex Numbers**

Polar Coordinates

Converting between polar and cartesian coordinates

Basics of vectors in cartesian coordiantes

Operations with vectors in cartesian coordiantes

Vectors in polar coordinates

Basics of Complex Numbers

More on Complex Numbers

De'Moivre's Theorem

**Unit 5 – Proofs by Mathematical Induction, The Fundamental Theorem of Algebra, and Intro to Linear Algebra**

Proofs by Mathematical Induction

Fundamental Theorem of Algebra

Intro to Linear Algebra and Matrices

Row Operations with Matrices

Row Echelon and Reduced Row Echelon Form

Coefficient Matrices

Guassian and Guass-Jordan Elimination

Basic Operations on Matrices

- Teacher: Sarah
- Areas of expertise: Secondary Mathematics
- Education: M.A. in Mathematics @ The University of Texas at Austin B.S. in Mathematics @ The University of Texas at Austin
- Interests: Outdoors, Sports, Arts & Crafts, Cooking, Mathematics
- Skills:
- Associations: National Council of Teachers of Mathematics
- Issues I care about:

This document includes and completed Unit Circle (with degrees, radians, and coordinates). Also, there is a tabular version that includes all six trig functions.

This document contains many formulas used with trigonometric functions. It will be referenced many times throughout the course.

Answers to Unit Circle Test.

Answers to Analytical Trigonometry Test.

Answers to Triangular Trig Test.

Answers to Polar Coordinates, Vectors, and Complex Numbers Test.

Answers to Proofs, Fund Thm, Linear Alg Test.