Trigonometry
Definition
The mathematics of triangles — especially right triangles — used in physics to split vectors into components and to analyze anything involving angles, from ramps to waves.
Technical definition
The study of relationships between angles and side lengths in triangles. The sine, cosine, and tangent functions relate an angle to ratios of sides in a right triangle and extend to periodic functions describing oscillations and waves.
Example
A 100 N force pulling at 30° above the horizontal splits into a horizontal component 100·cos30° ≈ 86.6 N and a vertical component 100·sin30° = 50 N — the standard trick for ramps, projectiles, and inclined planes.
The classic error is grabbing the wrong function: sine for the adjacent side instead of the opposite. Draw the triangle and label opposite/adjacent relative to your angle first — SOH-CAH-TOA only works if you identify the sides correctly. Also, calculators must be in degree mode when your angle is in degrees.