Trigonometry Essentials

This page serves as a comprehensive fiche de révision trigonométrie 3ème PDF, covering key concepts in trigonometry. It begins with angle conversions and progresses to properties of trigonometric functions and their notable values.

The document starts by explaining the conversion between degrees and radians. To convert degrees to radians, one divides by 180/π. An example is provided: 75° = 5π/12 radians. Conversely, to convert radians to degrees, one multiplies by 180/π. The example given is 7π/24 radians = 52.5°.

Example: 75° = 5π/12 radians, and 7π/24 radians = 52.5°

Next, the properties of cosine and sine functions are listed. These include:

• The range of cosine and sine: -1 ≤ cos$x$ ≤ 1 and -1 ≤ sin$x$ ≤ 1
• Evenness of cosine: cos$-x$ = cos$x$
• Oddness of sine: sin$-x$ = -sin$x$
• Periodicity: cos$x + 2π$ = cos$x$ and sin$x + 2π$ = sin$x$

Highlight: Cosine is an even function, while sine is an odd function.

A table of remarkable values is provided, showing the cosine and sine values for angles 0°, 30°, 45°, 60°, and 90° in both degrees and radians.

Vocabulary: Remarkable values are specific angle measures where trigonometric functions have exact, easily remembered values.

The document also touches on the concept of even and odd functions, relating it to the behavior of cosine and sine functions when the angle is negated.

Definition: An even function is symmetric about the y-axis, while an odd function is symmetric about the origin.

Finally, the page references the unit circle, noting that cosine represents the x-coordinate (abscissa) and sine represents the y-coordinate (ordinate) of a point on the unit circle.

Highlight: The unit circle is a fundamental tool in trigonometry, visually representing the relationship between angles and trigonometric ratios.

This fiche de révision trigonométrie 3ème serves as an excellent resource for students preparing for exercice trigonométrie 3ème or looking to reinforce their understanding of basic trigonometric concepts.