Cosine and Sine Functions of Real Numbers

This section delves into the properties of cosinus et sinus d'un nombre réel. The mathematical definitions and key properties are thoroughly explained.

Definition: For any real number x:

• cos(x) is defined as the x-coordinate of the point on the unit circle
• sin(x) is defined as the y-coordinate of the point on the unit circle

Highlight: Key properties include:

1. Domain restrictions: -1 ≤ cos(x) ≤ 1 and -1 ≤ sin(x) ≤ 1
2. Fundamental identity: cos²(x) + sin²(x) = 1
3. Periodicity: cos(x) = cos(x + 2kπ) and sin(x) = sin(x + 2kπ) for any integer k

Example: A comprehensive table of values is provided showing valeurs cosinus, sinus for standard angles, including special values like cos(0) = 1 and sin(π/2) = 1.

Vocabulary: Periodic function - A function that repeats its values at regular intervals.