Trigonometry Basics

Right-angled triangles have three sides with specific names that depend on which angle you're focusing on. The hypotenuse is always the longest side - it's opposite the right angle and never changes its name.

The other two sides change names depending on your angle of interest. The opposite side sits directly across from your chosen angle, whilst the adjacent side sits right next to it (but it's not the hypotenuse).

The three main trigonometric ratios help you find missing sides and angles. SOH CAH TOA is your best friend here: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. A handy trick is to cover what you want to find in the triangle - this shows you which sides to multiply or divide.

Quick Tip: Always label your triangle sides first (H, O, A) before picking which ratio to use - it prevents silly mistakes!

Exact trigonometric values for special angles (0°, 30°, 45°, 60°, 90°) pop up constantly in exams. Sin values start at 0 and climb to 1, whilst Cos values do the opposite. Tan starts at 0, hits 1 at 45°, then shoots up to √3 at 60° before becoming undefined at 90°.