﻿ Precalculus: the Mathematics of Numbers, Functions and Equations Archives - FutureLearn

## Glossary

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. …

## prova

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

## Final summary step

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 – …

## Systems of linear inequalities in practice

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 …

## Systems of linear inequalities

Graphical description of the solution sets

## Lines in the plane in practice

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 …

## Lines in the plane

Algebraic description of lines, connection to affine functions

## Inequalities with absolute values in practice

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 …

## Inequalities with absolute values

Analysis by cases, two special inequalities

## Inequalities with radicals in practice

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

## Polynomial inequalities in practice

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 …

## Polynomial inequalities

Relationship to roots, table of variations

## The quadratic case in practice

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 …