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Precalculus & Trigonometry Explained

Master Pre-calculus & Trigonometry with our Step by Step Video Tutorials. Over 1200 Practice Questions! Ace your Exam!
Instructor:
John Greene, M.A.
30 students enrolled
English [Auto]
Functions and Their Graphs
The Rectangular Coordinate Plane
Midpoint of a Line Segment
The Pythagorean Formula
Complex Plane - Distance and Midpoint Formulas
Absolute Value of a Complex Number
Vertices of a Right Triangle Formula
Collinear Points Formula
Equations of Circles
Function Definition
Domain and Range of Relations and Functions
Vertical Line Test
Function Notation
Graphing Linear Functions
Finding the Slope of a Line
Finding the Equation of a Line
Parallel and Perpendicular Lines
Graphs of Basic Functions
Piecewise-Defined Functions
Increasing, Decreasing, and Constant Intervals
Graphing Transformations - stretching, shrinking, reflecting
Graphing Transformations - horizontal and vertical shifts
Even and Odd Functions
Finding the Difference Quotient
Function Composition
Polynomial and Rational Functions
Finding the Vertex Form of a Parabola
Graphing Parabolas
The Remainder Theorem
The Factor Theorem
The Rational Zeros Theorem
The Fundamental Theorem of Algebra
Conjugate Zeros Theorem
Descartes' Rule of Signs
Intermediate Value and Boundedness Theorems
Finding the Zeros of a Polynomial Function
Exponential and Logarithmic Functions
The Horizontal Line Test
Finding One-to-One Functions Algebraically
Finding the Inverse of a Function
Proving that two functions are inverses
Domain Restrictions, Finding the Inverse
Exponential Functions and Their Graphs
Solving Exponential Equations without Logs
Solving Compound Interest Formula Word Problems
Solving Continuous Compound Interest Formula Word Problems
Logarithmic Functions
Properties of Logarithms
Inverse of an Exponential / Logarithmic Function
Evaluating Logarithms Using the Change of Base Formula
Solving Exponential Equations with Logarithms
Solving Logarithmic Equations
Systems of Equations and Inequalities
Solving Linear Systems in Two Variables
Solving Linear Systems in Three Variables
FInding the Equation of a Parabola Given Three Points
Linear Systems Word Problems
Partial Fraction Decomposition
Solving Nonlinear Systems of Equations
Solving Nonlinear Systems of Inequalities
Matrices and Determinants
Gauss-Jordan Elimination
Matrix Addition and Subtraction
Scalar Multiplication
Matrix Multiplication
Inverse of a Matrix
Matrix Equations
Determinants Using Laplace Expansion
Determinants Using Triangular Form
Transpose of a Matrix
Adjugate of a Matrix
Inverse Using the Adjugate and Determinant
Cramer's Rule
Area of a Triangle - Determinants
Collinear Points - Determinants
Writing the Equation of a Line - Determinants
Analytic Geometry
Conic Sections
The Parabola
The Ellipse
The Hyperbola
Sequences
Series
Summation Notation
Arithmetic Sequence
Arithmetic Series
Geometric Sequence
Geometric Series
Combinations
Permutations
Counting Theory
Angles
Acute Angles, Obtuse Angles, Right Angles, Straight Angles
Finding the Complement of an angle
Finding the Supplement of an angle
Degrees, Minutes, and Seconds
Converting Between Decimal Degrees and Degrees, Minutes, and Seconds
Determine if two Angles are Coterminal Angles
Solving for Missing Angles in Similar Triangles
Solving for Missing Sides in Similar Triangles
Solving for Missing Angles with a Transversal Crossing Two Parallel Lines
Finding the Trigonometric Function Values of an Angle
Finding Trigonometric Function Values Given One Value and the Quadrant
Finding Trigonometric Function Values Based on Reciprocal Identities
Finding Trigonometric Function Values Based on Pythagorean Identities
Finding Trigonometric Function Values Based on Quotient Identities
Finding the Six Trigonometric Function Values of an Acute Angle
Writing a Trigonometric Function in Terms of its Cofunction
Solving Trigonometric Equations using Cofunction Identities
Finding Reference Angles
Special Angles as Reference Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values of Non-Acute Angles

Become a Master of Pre Calculus & Trigonometry and Ace your next Exam! In this course, you will master the concepts of PreCalculus from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 1100 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. The topics of the course include:

  • Functions and Their Graphs

  • The Rectangular Coordinate Plane

  • Midpoint of a Line Segment

  • The Pythagorean Formula

  • Complex Plane – Distance and Midpoint Formulas

  • Absolute Value of a Complex Number

  • Vertices of a Right Triangle Formula

  • Collinear Points Formula

  • Equations of Circles

  • Function Definition

  • Domain and Range of Relations and Functions

  • Vertical Line Test

  • Function Notation

  • Graphing Linear Functions

  • Finding the Slope of a Line

  • Finding the Equation of a Line

  • Parallel and Perpendicular Lines

  • Graphs of Basic Functions

  • Piecewise-Defined Functions

  • Increasing, Decreasing, and Constant Intervals

  • Graphing Transformations – stretching, shrinking, reflecting

  • Graphing Transformations – horizontal and vertical shifts

  • Even and Odd Functions

  • Finding the Difference Quotient

  • Function Composition

  • Polynomial and Rational Functions

  • Finding the Vertex Form of a Parabola

  • Graphing Parabolas

  • The Remainder Theorem

  • The Factor Theorem

  • The Rational Zeros Theorem

  • The Fundamental Theorem of Algebra

  • Conjugate Zeros Theorem

  • Descartes’ Rule of Signs

  • Intermediate Value and Boundedness Theorems

  • Finding the Zeros of a Polynomial Function

  • Exponential and Logarithmic Functions

  • The Horizontal Line Test

  • Finding One-to-One Functions Algebraically

  • Finding the Inverse of a Function

  • Proving that two functions are inverses

  • Domain Restrictions, Finding the Inverse

  • Exponential Functions and Their Graphs

  • Solving Exponential Equations without Logs

  • Solving Compound Interest Formula Word Problems

  • Solving Continuous Compound Interest Formula Word Problems

  • Logarithmic Functions

  • Properties of Logarithms

  • Inverse of an Exponential / Logarithmic Function

  • Evaluating Logarithms Using the Change of Base Formula

  • Solving Exponential Equations with Logarithms

  • Solving Logarithmic Equations

  • Systems of Equations and Inequalities

  • Solving Linear Systems in Two Variables

  • Solving Linear Systems in Three Variables

  • FInding the Equation of a Parabola Given Three Points

  • Linear Systems Word Problems

  • Partial Fraction Decomposition

  • Solving Nonlinear Systems of Equations

  • Solving Nonlinear Systems of Inequalities

  • Matrices and Determinants

  • Gauss-Jordan Elimination

  • Matrix Addition and Subtraction

  • Scalar Multiplication

  • Matrix Multiplication

  • Inverse of a Matrix

  • Matrix Equations

  • Determinants Using Laplace Expansion

  • Determinants Using Triangular Form

  • Transpose of a Matrix

  • Adjugate of a Matrix

  • Inverse Using the Adjugate and Determinant

  • Cramer’s Rule

  • Area of a Triangle – Determinants

  • Collinear Points – Determinants

  • Writing the Equation of a Line – Determinants

  • Analytic Geometry

  • Conic Sections

  • The Parabola

  • The Ellipse

  • The Hyperbola

  • Sequences

  • Series and Summation Notation

  • Finding the nth term for an arithmetic sequence

  • Finding the nth term for a geometric sequence

  • Evaluating arithmetic series

  • Evaluating infinite and finite geometric series

  • Counting Theory

  • Combinations

  • Permutations

  • Angles in Trigonometry

  • Measuring angles using degrees

  • Complementary angles

  • Supplementary angles

  • Degrees, Minutes, and Seconds

  • Converting Between Decimal Degrees and Degrees, Minutes, and Seconds

  • Determine if two Angles are Coterminal Angles

  • Relationships between Angles: Vertical Angles, Angles formed by a Transversal and Parallel Lines

  • Solving for the Missing Angle Measurements with Similar Triangles

  • Solving for the Missing Lengths with Similar Triangles

  • Finding the Trigonometric Function Values of an Angle

  • Finding Trigonometric Function Values Given One Value and the Quadrant

  • Finding Trigonometric Function Values Based on Reciprocal Identities

  • Finding Trigonometric Function Values Based on Pythagorean Identities

  • Finding Trigonometric Function Values Based on Quotient Identities

  • Finding Trigonometric Function Values of an Acute Angle

  • Writing a Function in Terms of its Cofunction

  • Solving Equations Using Cofunction Identities

  • Finding Reference Angles

  • Special Angles as Reference Angles

  • Finding Angle Measures with Special Angles

  • Finding Trigonometric Function Values of Non-Acute Angles

Functions and Their Graphs

1
Rectangular Coordinate Plane

In this lesson, we will cover the basics of the coordinate plane.

2
Rectangular Coordinate Plane Practice Test
3
The Complex Plane and Plotting Complex Numbers

In this lesson, we review the complex plane and how to plot complex numbers.

4
The Complex Plane and Plotting Complex Numbers Practice Test
5
Midpoint of a Line Segment

In this lesson, we learn how to find the midpoint of a line segment.

6
Midpoint of a Line Segment Practice Test
7
The Pythagorean Formula and the Distance Between Two Points

In this lesson, we will learn how to use the distance formula, to find the distance between two points on the coordinate plane.

8
The Pythagorean Formula and The Distance Between Two Points Practice Test
9
Complex Plane - Distance and Midpoint Formulas

In this lesson, we learn how to find the distance between two points in the complex plane. Additionally, we learn how to find the midpoint of a line segment in the complex plane.

10
Complex Plane - Distance and Midpoint Formulas Practice Test
11
Absolute Value of a Complex Number

In this lesson, we learn how to find the absolute value of a complex number.

12
Absolute Value of a Complex Number Practice Test
13
Applications of The Distance Formula (Vertices of a Right Triangle)

In this lesson, we will learn how to use the distance formula to determine if three points are the vertices of a right triangle.

14
Applications of The Distance Formula (Vertices of a Right Triangle)Practice Test
15
Applications of The Distance Formula (Collinear Points)

In this lesson, we will learn how to use the distance formula to determine if three points are collinear.

16
Applications of The Distance Formula (Collinear Points) Practice Test
17
Equations of Circles

In this lesson, we will learn how to find the equation of a circle, as well as learn about the equation of a circle in general and standard form.

18
Equations of Circles Practice Test
19
Function Definition

In this lesson, we learn about the definition of a relation and the definition of a function.

20
Function Definition Practice Test
21
Domain and Range

In this lesson, we learn about the domain or the set of allowable x-values and the range or the set of allowable y-values.

22
Domain and Range Practice Test
23
Vertical Line Test

In this lesson, we learn about the vertical line test. This test allows us to determine if a relation is a function.

24
Vertical Line Test Practice Test
25
Function Notation

In this lesson, we learn how to use function notation.

26
Function Notation Practice Test
27
Graphing Linear Functions

In this lesson, we learn how to graph linear functions.

28
Graphing Linear Functions Practice Test
29
Finding the Slope of a Line

In this lesson, we learn how to find the slope of a line.

30
Finding the Slope of a Line Practice Test
31
Finding the Equation of a Line

In this lesson, we learn how to write the equation of a line in slope-intercept form, point-slope form, and standard form.

32
Finding the Equation of a Line Practice Test
33
Parallel and Perpendicular Lines
34
Parallel and Perpendicular Lines Practice Test
35
Graphs of Basic Functions

In this lesson, we will learn how to sketch the graphs of basic functions.

36
Graphs of Basic Functions Practice Test
37
PIecewise-Defined Functions

In this lesson, we will learn about piecewise-defined functions, or functions that have different definitions across the domain.

38
Piecewise-Defined Functions Practice Test
39
Increasing, Decreasing, & Constant Intervals

In this lesson, we will learn about increasing, decreasing, and constant intervals.

40
Increasing, Decreasing, & Constant Intervals Practice Test
41
Graphing Transformations: Stretching/Shrinking a Graph

In this lesson, we will learn about stretching or shrinking a graph.

42
Graphing Transformations: Stretching/Shrinking a Graph Practice Test
43
Graphing Transformations: Reflecting a Graph Across and Axis
44
Graphing Transformations: Reflecting a Graph Across and Axis Practice Test
45
Graphing Transformations: Horizontal and Vertical Shifts

In this lesson, we will learn about horizontal and vertical shifts.

46
Graphing Transformations: Horizontal and Vertical Shifts Practice Test
47
Even and Odd Functions

In this lesson, we will learn about even and odd functions.

48
Even and Odd Functions Practice Test
49
Operations with Functions

In this lesson, we will learn about performing operations with functions.

50
Operations with Functions Practice Test
51
Finding the Difference Quotient

In this lesson, we will learn how to find the difference quotient.

52
Finding the Difference Quotient Practice Test
53
Function Composition

In this lesson, we will learn about function composition.

54
Function Composition Practice Test

Polynomial Functions

1
Finding the Vertex Form of a Parabola

In this lesson, we will learn how to find the vertex form of a parabola.

2
Finding the Vertex Form of a Parabola Practice Test
3
Graphing Parabolas

In this lesson, we will learn the various techniques available for sketching the graph of a parabola.

4
Graphing Parabolas Practice Test
5
The Remainder Theorem

In this lesson, we will learn about the remainder theorem.

6
The Remainder Theorem Practice Test
7
The Factor Theorem

In this lesson, we will learn about the factor theorem.

8
The Factor Theorem Practice Test
9
The Rational Zeros Theorem

In this lesson, we will learn about the rational zeros theorem.

10
The Rational Zeros Theorem Practice Test
11
The Fundamental Theorem of Algebra

In this lesson, we will learn about the fundamental theorem of algebra.

12
The Fundamental Theorem of Algebra Practice Test
13
Conjugate Zeros Theorem

In this lesson, we will learn about the conjugate zeros theorem.

14
Conjugate Zeros Theorem Practice Test
15
Descartes' Rule of Signs

In this lesson, we will learn about Descartes' Rule of Signs.

16
Descartes' Rule of Signs Practice Test
17
Intermediate Value and Boundedness Theorems

In this lesson, we will learn about the intermediate value and boundedness theorems.

18
Intermediate Value and Boundedness Theorems Practice Test
19
Zeros of Polynomial Functions

In this lesson, we will learn how to find the zeros of polynomial functions.

20
Zeros of Polynomial Functions Practice Test

Exponential / Logarithmic Functions and Their Graphs

1
The Horizontal Line Test

In this lesson, we will learn how to use the horizontal line test to determine if a function is one-to-one.

2
The Horizontal Line Test Practice Test
3
Finding One-to-One Functions Algebraically

In this lesson, we will learn how to determine if a function is one-to-one using an algebraic method.

4
Finding One-to-One Functions Algebraically Practice Test
5
Finding the Inverse of a Function
6
Finding the Inverse of a Function Practice Test
7
Prove that Two Functions are Inverses

In this lesson, we will learn how to determine if two functions are inverses using function composition.

8
Prove that Two Functions are Inverses Practice Test
9
Domain Restrictions, Finding the Inverse

In this lesson, we will learn how to find the inverse of a domain restricted function.

10
Domain Restrictions, Finding the Inverse Practice Test
11
Exponential Functions and Their Graphs

In this lesson, we will learn about exponential functions.

12
Exponential Functions and Their Graphs Practice Test
13
Solving Exponential Equations without Logs

In this lesson, we will learn how to solve exponential equations when logarithms are not required.

14
Solving Exponential Equations without Logs Practice Test
15
Solving Compound Interest Formula Word Problems

In this lesson, we will learn how to solve word problems that involve the compound interest formula.

16
Solving Compound Interest Formula Word Problems Practice Test
17
Solving Continuous Compound Interest Formula Word Problems

In this lesson, we learn how to solve word problems that involve the continuous compound interest formula.

18
Solving Continuous Compound Interest Formula Word Problems Practice Test
19
Logarithmic Functions

In this lesson, we will learn how to work with logarithmic functions.

20
Logarithmic Functions Practice Test
21
Properties of Logarithms

In this lesson, we will learn about the properties of logarithms, the product property, quotient property, and power property.

22
Properties of Logarithms Practice Test
23
Inverse of an Exponential / Logarithmic Function

In this lesson, we will learn how to find the inverse of an exponential / logarithmic function.

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