Course: Precalculus: the Mathematics of Numbers, Functions and Equations

We are planning to prepare a Glossary that contains a list of the key terms that are used in the course. Many of them are defined in the next steps. …

\[\sin(x)+\cos(x)\leq\frac{1}{\sin(x)}\iff \frac{1}{\sin(x)}-\sin(x)-\cos(x)\geq 0 \iff \frac{1-\sin^2(x)-\sin(x)\cos(x)}{\sin(x)}\geq 0\] \[\iff \frac{\cos^2(x)-\sin(x)\cos(x)}{\sin(x)}\geq 0\iff\cot(x)(\cos(x)-\sin(x))\geq 0.\]

Congratulations! You have reached the end of the course. You should have become acquainted with: Numbers, Functions, Equations and Inequalities. Alberto is telling us that you now love Algebra – …

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Graphical description of the solution sets

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Algebraic description of lines, connection to affine functions

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Analysis by cases, two special inequalities

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

The case of two radicals

Two main types of inequalities, two sorts of equivalence

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …

Relationship to roots, table of variations

The following exercises are solved in this step. We invite you to try to solve them before watching the video. In any case, you will find below a PDF file …