## The bases of the Euclidean plane: vectors and coordinates

The representation of the Euclidean plane as the Cartesian product \(\mathbb R^2\) allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This

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# trigonometric circle

## The bases of the Euclidean plane: vectors and coordinates

## Vector rotations of the plane: the analytical approach

## The Trigonometric Circle: where Pythagoras meets Thales

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The representation of the Euclidean plane as the Cartesian product \(\mathbb R^2\) allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This

The vector rotations of the plane (i.e. centred in the origin), are derived analytically (by coordinates) as linear applications of determinant \(1\), which makes it possible to characterise them integrally

The trigonometric circle allows us to define the cosine, sine and tangent of an oriented angle, and to give an interpretation through Thales' and Pythagoras' theorems.
Introduction: trigonometry and functions
Trigonometry is