SOH-CAH-TOA is a helpful way to remember the main trigonometric ratios for a right triangle.

Here’s what each part means:

• SOH: Sine = Opposite side / Hypotenuse
• CAH: Cosine = Adjacent side / Hypotenuse
• TOA: Tangent = Opposite side / Adjacent side

Knowing these ratios is really important in AS-Level Maths because they connect to different ideas like:

1. Angles and Measurements: We use trigonometric ratios for angles in both degrees and radians.

2. Graphs of Trigonometric Functions: We can draw graphs for sine, cosine, and tangent to see how they change and relate to angles.

3. Solving Triangles: With SOH-CAH-TOA, you can find unknown lengths and angles in right triangles.

For instance, let’s say we have a right triangle where the angle ( \theta ) has an opposite side that measures 3 and a hypotenuse that measures 5. To find the sine, we can use the formula:

$\sin(\theta) = \frac{3}{5}$

This shows how SOH-CAH-TOA helps us understand more complicated trigonometric ideas!