Precalculus

Overview

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Dive into a comprehensive 5-hour precalculus course covering a wide range of mathematical concepts. Explore functions, including increasing and decreasing functions, maximums and minimums on graphs, even and odd functions, and toolkit functions. Learn about transformations, piecewise functions, and inverse functions. Study angles, arclength, and areas of sectors. Delve into trigonometry, covering right angle trigonometry, special angles, unit circle definitions, and properties of trigonometric functions. Examine graphs of various trigonometric functions and their transformations. Master trigonometric equations, identities, and formulas, including Pythagorean identities, angle sum and difference formulas, and double and half angle formulas. Apply knowledge to solving triangles using the Law of Cosines and Law of Sines. Explore conic sections, including parabolas, ellipses, and hyperbolas. Conclude with an introduction to polar coordinates, parametric equations, and the difference quotient.

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 OLD VERSION.
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.
Graphs of Transformations of Tan, Sec, Cot, Csc.
Inverse Trig Functions.
Solving Basic Trig Equations.
Solving Trig Equations that Require a Calculator.
Trig Identities.
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.