Ecrire les formules de trigonométrie (cos, sin, tan) - Troisième

Introduction

This tutorial provides a step-by-step guide on writing trigonometric formulas for cosine, sine, and tangent in a right triangle. Understanding these formulas is essential for solving various problems in geometry, physics, and engineering.

Step 1: Understanding the Right Triangle

• A right triangle has one angle measuring 90 degrees.
• The sides of the triangle are classified as:
  • Hypotenuse: The longest side opposite the right angle.
  • Opposite side: The side opposite the angle you are analyzing.
  • Adjacent side: The side next to the angle you are analyzing, excluding the hypotenuse.

Step 2: Writing the Sine Formula

• The sine of an angle (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
• Formula: [ \sin(A) = \frac{\text{Opposite}}{\text{Hypotenuse}} ]

Step 3: Writing the Cosine Formula

• The cosine of an angle (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
• Formula: [ \cos(A) = \frac{\text{Adjacent}}{\text{Hypotenuse}} ]

Step 4: Writing the Tangent Formula

• The tangent of an angle (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side.
• Formula: [ \tan(A) = \frac{\text{Opposite}}{\text{Adjacent}} ]

Step 5: Applying the Formulas

• To solve problems involving right triangles:
  • Identify the angle and the relevant sides.
  • Use the appropriate formula based on the sides you know.
  • Substitute the known values into the formula and solve for the unknown.

Practical Tips

• Always label the sides of the triangle to avoid confusion.
• Make sure to use the correct angle when applying the formulas.
• Familiarize yourself with the unit circle for a deeper understanding of sine, cosine, and tangent values.

Common Pitfalls to Avoid

• Confusing the opposite and adjacent sides.
• Forgetting to simplify the ratios when possible.
• Not using a calculator properly when dealing with angles in radians or degrees.

Conclusion

In this tutorial, you learned how to write and apply the trigonometric formulas for sine, cosine, and tangent in a right triangle. These formulas are fundamental tools in mathematics and can be applied to various real-world scenarios. Practice using these formulas with different triangle problems to solidify your understanding.