Download Udemy – College Algebra, Pre-Calculus, & Trigonometry Explained 2023-11

Review of basic concepts: real numbers, order of operations, number line, absolute value

Examining polynomials: addition, subtraction, multiplication, division, artificial division, factoring

Examining rational expressions: least expressions, undefined, addition, subtraction, multiplication, division, mixed fractions

Examining Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators

Solving linear equations and inequalities

Solving application problems of linear equations (word problems)

Solving absolute value equations and inequalities

Working with mixed numbers

Solving quadratic equations and inequalities

Solving applications of quadratic equations (word problems)

Solving exponential equations and inequalities

Solving radical equations and inequalities

Rectangular coordinate plane

Complex coordinate plane

Distance and midpoint formulas

Relationships and functions

Scope and scope

Function notation, function composition, operations on functions

Graph of linear equations

Linear equations, finding the slope of a line and equations of lines

Diagrammatic circles

Diagram of elementary functions

Graphical transformations

Solving the system of linear equations in two variables

Solving the system of linear equations in three variables

Solving word problems with linear systems

Use curve fitting to find the equation through three points

Partial fraction decomposition

Solving linear systems using Gauss elimination and Gauss-Jordan elimination

Addition and subtraction of matrices

Solving matrix equations

Multiplying a matrix by a scalar

Finding the inverse of a matrix

Solving linear systems using matrix inversion

Determine whether the functions are one-to-one using the horizontal line test

Determine whether the functions are algebraically one-to-one

Find the inverse of the one-to-one function

Find the inverse of the bounded one-to-one function of the domain

Inverse graph of a function

Draw the graph of an exponential function

Solving exponential equations with similar bases

Solving compound interest word problems

Drawing the graph of logarithmic functions

Properties of logarithms Dense logarithms Expansion of logarithms

Change of base rule for logarithms

Solving exponential and logarithmic equations

Solving exponential and logarithmic inequalities

Applications of exponential and logarithmic functions

Find the shape of the vertex of a parabola

How to draw a parabolic graph

The remaining case

Use the remainder theorem to test zeros for a polynomial function

Using the factor theorem to factorize a polynomial function with a zero

The theorem of rational zeros

The fundamental theorem of algebra

Writing zero and one point polynomial equations

Conjugate Zeros Theorem

Descartes’ law of signs

Average value theorem

Finding upper and lower bounds for the real zeros of a polynomial function

Solving nonlinear systems of equations

Conic Sections: Parabolas – Focus and Directrix

Conic Sections: Ellipses – Find the foci and graph

Arithmetic sequences

Geometric sequences

Finding the common difference in an arithmetic sequence

Evaluation of an arithmetic series

Binomial theorem

Working with sets, list method, subsets, Venn diagrams

Angles in trigonometry

Complementary angles

Determine whether two angles are coterminal angles

Find angle measures for similar triangles

Find side lengths for similar triangles

Finding the values ​​of the trigonometric function of an angle

Finding values ​​of trigonometric function with one value and quadrant

Finding trigonometric function values ​​based on mutual identities

Finding trigonometric function values ​​based on Pythagorean identities

Finding the values ​​of the trigonometric function based on the quotient identities

Finding the values ​​of the trigonometric function of acute angles

Writing a trigonometric function in terms of its common function

Solving trigonometric equations using functional identities

Find reference angles

Special angles as reference angles

Find angle measures with certain angles

Finding the trigonometric function values ​​of non-acute angles

Find the values ​​of the trigonometric function using a calculator

Find unknown angle measures using inverse trigonometric functions: arcsin, arccos, arctan

Solving a right triangle

Solve word problems involving elevation angles

Solve word problems that include depression angles

Radian measurement

Convert between degrees and radians

How to find the length of an arc in a circle

How to find the area of ​​a segment of a circle

Definition of six trigonometric functions using the unit circle

Working with circular functions

Solving trigonometric word problems involving linear velocity

Solving trigonometric word problems involving angular velocity

Draw a sine and cosine graph

Transform functions with sine and cosine

Find period, amplitude and phase shift

Using fundamental trigonometric identities to find missing trigonometric ratios

Using fundamental trigonometric identities to rewrite trigonometric expressions

How to verify trigonometric identity

Sum and difference identity for sine, cosine and tangent

Finding Sin (A + B)

Find Tan (A + B)

Two angle identities

Collective product identity

The identity of the product

Half-angle identities

Evaluation of inverse trigonometric functions

Draw the graph of inverse trigonometric functions

Find the combination of inverse trigonometric functions

Solving trigonometric equations using linear methods

Solving trigonometric equations by factoring

Solving trigonometric equations with squares/square roots

Solving trigonometric equations using identity

Solving trigonometric equations using quadratic formula

Solving trigonometric equations with half angles

Solving trigonometric equations with several angles

Solving trigonometric equations including inverse trigonometric functions

Law of sines

law of sines (ambiguous case)

Triangle area using sine (SAS) and (ASA)

Law of cosines

Triangle area using Heron’s formula

Finding the form of the components of a vector

Find the magnitude of a vector

Find the direction angle of a vector

Find the sum (result) of two vectors

Multiply vector by scalar

Find the unit vector

Write a linear combination of unit vectors

Find the dot product of two vectors

Find the angle between the two vectors

Determine whether two vectors are orthogonal

Adding two complex numbers graphically

Finding the trigonometric (polar) form of a complex number

Complex number conversion between rectangular and polar shapes

Multiply complex numbers in polar form

Division of complex numbers in polar form

Product and quotient theorems

Power of complex numbers in polar form

Solving equations using roots of complex numbers

Plotting points on the polar coordinate grid

Convert points between rectangular and polar shapes

Writing polar coordinates in alternate forms

Find the distance between two polar points

Convert a line between polar and rectangular shapes

Draw a line on the polar grid

Find the slope of a line

Find the angle between two lines

Find the shortest distance between a line and a point