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## The derivative of a function: definition and geometric interpretation

The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point. 1. General idea: an instantaneous variation We place ourselves here in the framework of functions of a real...

## Linear transformations of the plane: determinant, bases and inversion

The linear transformations of the Euclidean plane are the invertible linear applications, i.e. of non-zero determinant. They allow us to move from one basis of the plane to another, and the orthogonal transformations, i.e. the vectorial isometries, exchange the...

## 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 decomposition is linked to a particular and natural “representation...

## The Trigonometric Circle: where Pythagoras meets Thales

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 the study of the relationships...