Explore essential mathematical concepts in this comprehensive 3.5-hour tutorial covering calculus prerequisites. Master rational expressions, difference quotients, and line equations before delving into trigonometry, including special angles, unit circles, and function properties. Analyze graphs of various trigonometric functions, solve equations, and learn key identities. Progress to function composition, rational equations, and logarithms, understanding their rules and applications. Investigate inverse functions, both general and trigonometric, and tackle polynomial inequalities. Conclude with an introduction to summation notation, preparing you for advanced calculus topics.
Overview
Syllabus
Rational Expressions.
Difference Quotient.
Lines: Graphs and Equations.
Rational Functions and Graphs.
Right Angle Trigonometry.
Sine and Cosine of Special Angles.
Unit Circle Definition of Sine and Cosine.
Properties of Trig Functions.
Graphs of Sine and Cosine.
Graphs of Sinusoidal Functions.
Graphs of Tan, Sec, Cot, Csc.
Solving Basic Trig Equations.
Trig Identities.
Pythagorean Identities.
Angle Sum and Difference Formulas.
Double Angle Formulas.
Composition of Functions.
Solving Rational Equations.
Logarithms: Introduction.
Log Functions and Their Graphs.
Combining Logs and Exponents.
Log Rules.
Inverse Functions.
Inverse Trig Functions.
Solving Right Triangles.
Polynomial and Rational Inequalities.
Summation Notation.
Taught by
Linda Green
