Embark on a comprehensive 4-hour 49-minute precalculus video course designed to prepare students for calculus studies. Dive deep into essential topics including functions, trigonometry, and conic sections. Explore concepts such as increasing and decreasing functions, maximums and minimums on graphs, even and odd functions, and transformations. Master trigonometric principles including right angle trigonometry, special angles, unit circle definitions, and inverse functions. Delve into advanced topics like laws of cosines and sines, parabolas, ellipses, hyperbolas, polar coordinates, and parametric equations. Benefit from clear explanations by Prof. Linda Green, covering everything from basic function properties to complex trigonometric identities and formulas. Perfect for beginners seeking a solid foundation in precalculus, this course offers a structured approach with a detailed table of contents for easy navigation through various mathematical concepts.
Overview
Syllabus
Functions.
Increasing and Decreasing Functions.
Maximums and minimums on graphs.
Even and Odd Functions.
Toolkit Functions.
Transformations of Functions.
Piecewise Functions.
Inverse Functions.
Angles and Their Measures.
Arclength and Areas of Sectors.
Linear and Radial Speed.
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.
Inverse Trig Functions.
Pythagorean Identities.
Angle Sum and Difference Formulas.
Proof of the Angle Sum Formulas.
Double Angle Formulas.
Half Angle Formulas.
Solving Right Triangles.
Law of Cosines.
Law of Cosines - old version.
Law of Sines.
Parabolas - Vertex, Focus, Directrix.
Ellipses.
Hyperbolas.
Polar Coordinates.
Parametric Equations.
Difference Quotient.
Taught by
Academic Lesson
