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.

Introduction to Trigonometric Functions and Radian Measurements

This introductory section establishes the fundamental concepts of trigonometric functions in a coordinate plane. The cercle trigonométrique is defined as a circle with center O and unit radius, oriented in the counterclockwise (direct) direction.

Definition: The trigonometric circle is a unit circle centered at O with radius 1, having a circumference of 2π.

Highlight: The relationship between degrees and radians is presented in a comprehensive conversion table, showing key angles from 0° to 360°.

Example: Common angle measurements are provided:

• 30° = π/6 radians
• 45° = π/4 radians
• 60° = π/3 radians
• 90° = π/2 radians

Vocabulary: Radian - The standard unit of angular measurement in trigonometry, where one complete rotation equals 2π radians.