Trigonometric Ratios

Vectors & Geometry · c. 150 BCE

Equation: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj, sin²θ + cos²θ = 1
Field: Vectors & Geometry
Symbols: θ an angle in a right triangle · opp, adj the sides opposite and adjacent to it · hyp the hypotenuse
Year: -150

Significance

The dictionary between angles and lengths. Snell's law, Bragg's law and the diffraction grating are each one line of trigonometry; so is resolving a force on an incline or laying out a roof pitch. Hipparchus tabulated chords around 150 BCE; the sine as we write it came from India in the fifth century and reached Europe through Arabic. The identity on the right is Pythagoras again.

Skills

Squaring with the 3-4-5 Rule

Required By

Dot Product Cross Product Law of Cosines Simple Harmonic Motion Snell's Law Bragg's Law Diffraction Grating Equation Capillary Rise Ninety-Degree Rule Ghost-Ball Aim Throw

Referenced by

equation

Bragg's Law Capillary Rise Cross Product Diffraction Grating Equation Dot Product Ghost-Ball Aim Law of Cosines Ninety-Degree Rule Simple Harmonic Motion Snell's Law Throw

skill

Squaring with the 3-4-5 Rule

Open on the Equations shelf — the interactive card, the filters, and everything alongside it.

From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.