Navigation

GPS, ship and aircraft routes

Latitude/longitude calculations use spherical trig — the "haversine formula" for great-circle distance is sine + cosine of half-angles.

Astronomy

distances to stars (parallax)

Distance to nearby stars uses parallax angles measured 6 months apart. Sin(angle) × Earth-orbit radius = light-years to the star.

Music

sound waves (sin curves)

A pure tone is sin(2π·frequency·t). Speech, instruments, even noise can be decomposed into sums of sines (Fourier).

Construction

roof slopes, ramp angles

A roof rafter at 30° pitch over a 4 m run rises 4 × tan(30°) = 2.31 m. Every angle in a building is a tangent calculation.

Surveying

heights of buildings without climbing

Theodolites measure angles; trigonometric levelling computes heights of mountains — that's how we know Everest is 8,848 m.

Engineering

AC current, vibrations

AC electricity is V(t) = V₀·sin(ωt). Phasors, impedance, three-phase power — all built on sin and cos.