Trigonometry studies the relationships between angles and sides of triangles. The three primary trigonometric ratios — sine, cosine, and tangent — relate an angle in a right triangle to ratios of its sides.

The mnemonic SOH CAH TOA helps you remember: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Trigonometric functions also apply to the unit circle, where any angle θ maps to coordinates (cos θ, sin θ). This extends trigonometry beyond right triangles to all angles, including those greater than 90°.

Common angle values to memorize: sin(30°) = 1/2, sin(45°) = √2/2, sin(60°) = √3/2, cos(30°) = √3/2, cos(45°) = √2/2, cos(60°) = 1/2.