Precalculus & Trigonometry Explained
What you'll learn
- 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
- Finding Trigonometric Function Values Using a Calculator
- Finding Unknown Angle Measures Using Inverse Trigonometric Functions
- arcsin, arccos, arctan, arcsec, arccsc, arccot
- How to Solve Right Triangles When Two Sides are Known
- How to Solve Right Triangles Given an Angle and a Side
- How to Solve Word Problems that Involve Angles of Elevation
- How to Solve Word Problems that Involve Angles of Depression
- Radians
- Converting Between Radians and Degrees
- Finding Arc Length on a Circle
- Finding the Area of a Sector of a Circle
- Understanding Trigonometry Using the Unit Circle
- Circular Functions
- Solving Trigonometry word problems with Linear and Angular Speed
- Using the Fundamental Trigonometric Identities to Find Missing Trigonometric Ratios
- Using the Fundamental Trigonometric Identities to rewrite Trigonometric Expressions
- How to Verify Trigonometric Identities
- Sum and Difference Identities for Sine, Cosine, and Tangent
- Finding sin(A + B), sin(A - B)
- Finding cos(A + B), cos(A - B)
- Finding tan(A + B), tan(A - B)
- Double-Angle Identities
- Product-to-Sum Identities
- Sum-to-Product Identities
- Half-Angle Identities
- Solving Trigonometric Equations Using Linear Methods
- Solving Trigonometric Equations by Factoring
- Solving Trigonometric Equations by Squaring/Square Roots
- Solving Trigonometric Equations Using Identities
- Solving Trigonometric Equations Using the Quadratic Formula
- Solving Trigonometric Equations with Half-Angles
- Solving Trigonometric Equations with Multiple Angles
- Inverse Trigonometric Functions
- Sketching the Graphs of the Inverse Trigonometric Functions
- Evaluating Inverse Trigonometric Functions
- Finding the Composition of Inverse Trigonometric Functions
- Solving Trigonometric Equations with Inverse Trigonometric Functions
- Law of Sines (ASA) and (SAA)
- Finding the Area using sine (SAS)
- Law of Sines Ambiguous case
- Law of Cosines
- Finding the Area using Heron's Formula (SSS)
- Finding the Component Form of a Vector
- Finding the Magnitude of a Vector
- Finding the Direction Angle of a Vector
- Finding the Sum of Two Vectors
- Multiplying a Vector by a Scalar
- Finding the Unit Vector u in the direction of the Vector v
- Writing a Linear Combination of Unit Vectors i and j
- Find the Dot Product of Two Vectors
- Find the Angle Between Two Vectors
- Determine if Two Vectors are Orthogonal
Requirements
- Arithmetic (Must Have)
- Pre-Algebra (Must Have)
- Algebra 1 (Must Have)
- Algebra 2 (Must Have)
Description
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 1400 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
Finding Trigonometric Function Values Using a Calculator
Finding Unknown Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan
Solving Right Triangles
Solving Word Problems that involve angles of elevation
Solving Word Problems that involve angles of depression
Radian Measure
Converting between Radians and Degrees
Finding the Arc Length on a Circle
Finding the Area of a Sector of a Circle
The Unit Circle and Circular Functions
Solving Word Problems with Linear & Angular Speed
Using the Fundamental Identities to find missing Trigonometric Ratios
Using the Fundamental Identities to rewrite Trigonometric Expressions
Sum and Difference Identities for Sine, Cosine, and Tangent
Finding sin(A + B), cos(A + B), and tan(A + B)
Finding sin(A - B), cos(A - B), and tan(A - B)
Half-Angle Identities
Finding s/2 given information about s
Solving Trigonometric Equations Using Linear Methods
Solving Trigonometric Equations by Factoring
Solving Trigonometric Equations by Squaring/Square Roots
Solving Trigonometric Equations Using Identities
Solving Trigonometric Equations Using the Quadratic Formula
Solving Trigonometric Equations with Half-Angles
Solving Trigonometric Equations with Multiple Angles
Evaluating Inverse Trigonometric Functions
Sketching the Graphs of Inverse Trigonometric Functions
Finding the Composition of Inverse Trigonometric Functions
Solving Trigonometric Equations with Inverse Trigonometric Functions
Law of Sines (SAA) and (ASA)
Finding the Area of a triangle given (SAS) using sine
Law of Sines Ambiguous case
Law of Cosines
Finding the area of a triangle given (SSS) using Heron's Formula
Vectors
Finding the Component Form of a Vector
Finding the Magnitude of a Vector
Finding the Direction Angle of a Vector
Finding the Resultant (Sum) of Two Vectors
Multiplying a Vector by a Scalar
Find the Unit Vector u in the direction of the vector v
Write a linear combination of unit vectors i and j
Find the Dot Product
Find the Angle Between Two Vectors
Determine if Two Vectors are Orthogonal
Who this course is for:
- Students who want to master Precalculus
- Students who want to master Trigonometry
- Students who want to excel in Calculus
Course content
- 00:55Welcome to the Course :)
- Preview20:01
- 00:07Rectangular Coordinate Plane Practice Test
- 06:01The Complex Plane and Plotting Complex Numbers
- 00:07The Complex Plane and Plotting Complex Numbers Practice Test
- 17:14Midpoint of a Line Segment
- 00:07Midpoint of a Line Segment Practice Test
- 19:51The Pythagorean Formula and the Distance Between Two Points
- 00:07The Pythagorean Formula and The Distance Between Two Points Practice Test
- 18:46Complex Plane - Distance and Midpoint Formulas
- 00:07Complex Plane - Distance and Midpoint Formulas Practice Test
- Preview14:20
- 00:07Absolute Value of a Complex Number Practice Test
- 14:42Applications of The Distance Formula (Vertices of a Right Triangle)
- 00:07Applications of The Distance Formula (Vertices of a Right Triangle)Practice Test
- 14:15Applications of The Distance Formula (Collinear Points)
- 00:07Applications of The Distance Formula (Collinear Points) Practice Test
- 31:49Equations of Circles
- 00:07Equations of Circles Practice Test
- 20:43Function Definition
- 00:07Function Definition Practice Test
- 25:53Domain and Range
- 00:07Domain and Range Practice Test
- 15:29Vertical Line Test
- 00:07Vertical Line Test Practice Test
- 18:51Function Notation
- 00:07Function Notation Practice Test
- 27:51Graphing Linear Functions
- 00:07Graphing Linear Functions Practice Test
- 25:21Finding the Slope of a Line
- 00:07Finding the Slope of a Line Practice Test
- 24:09Finding the Equation of a Line
- 00:07Finding the Equation of a Line Practice Test
- 26:16Parallel and Perpendicular Lines
- 00:07Parallel and Perpendicular Lines Practice Test
- 20:15Graphs of Basic Functions
- 00:07Graphs of Basic Functions Practice Test
- 24:43PIecewise-Defined Functions
- 00:07Piecewise-Defined Functions Practice Test
- 20:22Increasing, Decreasing, & Constant Intervals
- 00:07Increasing, Decreasing, & Constant Intervals Practice Test
- 22:57Graphing Transformations: Stretching/Shrinking a Graph
- 00:07Graphing Transformations: Stretching/Shrinking a Graph Practice Test
- 30:08Graphing Transformations: Reflecting a Graph Across and Axis
- 00:07Graphing Transformations: Reflecting a Graph Across and Axis Practice Test
- 25:23Graphing Transformations: Horizontal and Vertical Shifts
- 00:07Graphing Transformations: Horizontal and Vertical Shifts Practice Test
- 30:02Even and Odd Functions
- 00:07Even and Odd Functions Practice Test
- 27:47Operations with Functions
- 00:07Operations with Functions Practice Test
- 20:07Finding the Difference Quotient
- 00:07Finding the Difference Quotient Practice Test
- 35:26Function Composition
- 00:07Function Composition Practice Test
Instructor
John Greene earned a bachelor's degree in Mathematics and a master's degree in Economics. Throughout his career, he has helped thousands of students ace their math and economics courses. John has a passion for learning, and wants to help students excel. John founded the site GreeneMath to help struggling students raise their grades in math, regardless of income.