Understanding the Unit Circle and Trigonometric Functions

The first page introduces fundamental concepts of trigonometry through the unit circle and its associated functions. The content covers essential properties, conversions, and mathematical relationships that form the basis of trigonometric calculations.

Definition: The unit circle (cercle trigonométrique) is defined as a circle with center O and radius 1, with counterclockwise rotation designated as the positive direction.

Highlight: Key properties of trigonometric functions include:

• cos(-x) = cos(x)
• sin(-x) = -sin(x)
• (cos x)² + (sin x)² = 1
• -1 ≤ cos(x) ≤ 1
• -1 ≤ sin(x) ≤ 1

Example: The conversion between degrees and radians follows the formula: x radians = (x × 180)/π degrees

Vocabulary: Principal measure (mesure principale) refers to the unique angle measure within the interval ]-π, π] that represents an angle's orientation.

Quote: "Les fonctions sinus et cosinus sont 2π-périodiques, c'est à dire qu'elles se répètent tous les 2π." (Sine and cosine functions are 2π-periodic, meaning they repeat every 2π)

The page also includes detailed trigonometric graphs showing the behavior of sine and cosine functions, emphasizing their periodic nature and symmetry properties. Special angle values and their corresponding trigonometric ratios are presented in both degree and radian measures, providing a comprehensive reference for calculations.