In AS-Level Mathematics, it's really important to understand the basic ideas behind trigonometric ratios. Let's look at the main concepts of sine, cosine, and tangent.

1. Sine ($\sin$): The sine of an angle in a right triangle is the relationship between the length of the opposite side and the hypotenuse (the longest side).

   You can think of it this way:

   $$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$$

   For example, if one side opposite the angle is 3 units long and the hypotenuse is 5 units long, then: $\sin(\theta) = \frac{3}{5}$.

2. Cosine ($\cos$): The cosine is about the relationship between the length of the adjacent side (the side next to the angle) and the hypotenuse.

   It looks like this:

   $$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$$

   So, if the adjacent side is 4 units and the hypotenuse is still 5 units, then: $\cos(\theta) = \frac{4}{5}$.

3. Tangent ($\tan$): The tangent describes the relationship between the opposite side and the adjacent side.

   It's written as:

   $$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$$

   Using our earlier example, if the opposite side is 3 units and the adjacent side is 4 units, then: $\tan(\theta) = \frac{3}{4}$.

These definitions help you get ready to solve different trigonometry problems in your classes!