Precalculus & Trigonometry Explained

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 1500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. This course is a more concise version of College Algebra & Trigonometry Explained. It provides a quicker path to get ready for college level math and assumes you are proficient in algebra 1 and algebra 2. 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

• Sketching the Graphs of Sine and Cosine

• Function Transformations with the Graphs of Sine and Cosine

• Finding the Period, Amplitude, Phase Shift, and Vertical Shift for Trigonometric Functions

• 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

• Finding the Sum of Two Complex Numbers Graphically

• Finding the Polar Form of a Complex Number

• Changing Between the Polar Form and Rectangular Form

• Multiplying Complex Numbers in Polar Form

• Dividing Complex Numbers in Polar Form

• Product and Quotient Theorems

• De Moivre's Theorem

• Powers of Complex Numbers in Polar Form

• Roots of Complex Numbers in Polar Form

• Solving Equations Using Roots of Complex Numbers

• The Polar Coordinate System

• Plotting Polar Coordinates on the Polar Plane

• Converting Between Polar and Rectangular Coordinates

• Writing Polar Coordinates in Multiple Forms

• Finding the Distance Between Polar Points

• Converting Between Polar and Rectangular Forms of a Line

• Graphing Lines on the Polar Plane

• Converting Between Polar and Rectangular Forms of a Circle

• Graphing Circles on the Polar Plane

• Finding the Inclination of a Line

• Finding the Angle Between Two Lines

• Finding the Distance Between a Point and a Line