by Jean Barbet | May 8, 2021 | Algebra, Geometry, Non classé
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... 
by Jean Barbet | Feb 20, 2021 | Functions, Number Theory
Introduction When we introduced the circular exponential, the trigonometric functions cosine and sine were defined as its real part and imaginary part. From this, we derived the analytical expressions: \(\cos x=\sum_{n=0}^{+\infty} (-1)^n\dfrac{x^{2n}}{(2n)!}\) and... 
by Jean Barbet | Jan 9, 2021 | Analysis, Functions, Non classé
From the complex exponential function, we can define a “circular exponential” function, which “wraps” the real line around the trigonometric circle, and makes it possible to rigorously define the cosine and sine trigonometric functions, which... 
by Jean Barbet | Oct 25, 2020 | Geometry, Non classé, Trigonometry
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...
