What are the basic trigonometric ratios and how are they used?

In Grade 9 mathematics in South Africa, students are introduced to basic trigonometric ratios: sine, cosine, and tangent. These ratios are used to calculate the relationships between the angles and sides of right-angled triangles.

The formulas for these ratios are:

• Sine: $\sin(\theta) = \frac{opposite}{hypotenuse}$
• Cosine: $\cos(\theta) = \frac{adjacent}{hypotenuse}$
• Tangent: $\tan(\theta) = \frac{opposite}{adjacent}$

Understanding and applying these ratios is essential for solving various real-world problems involving angles and distances.