Trigonometry: The Basics

SAT trigonometry starts with one shape: a right triangle, meaning a triangle with one $90°$ angle.

Pick one of the slanted angles and call it theta. Now the three sides get names. The hypotenuse is the longest side, always across from the right angle. The opposite side is across the triangle from theta. The adjacent side is the other leg, the one touching theta.

Three ratios follow, and one word holds all of them: SOH-CAH-TOA. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. Tangent is opposite over adjacent.

So the whole move is: label the three sides for your angle, then pick the ratio the question asks for.

A few values are worth memorizing, especially $\sin 30° = \frac{1}{2}$ and . And one identity is always true: .