TeXipedia

phi

Represents a mathematical variable or angle commonly used in physics, mathematics, and engineering applications.

Overview

A versatile Greek letter that appears frequently across multiple scientific disciplines and mathematical contexts.

  • Often used to denote angles in geometry and trigonometry
  • Common in physics for representing phase angles and electric potential
  • Appears in probability theory and statistics for various functions
  • Used in engineering to represent magnetic flux
  • Serves as a standard variable in mathematical proofs and equations where Greek letters are conventional

Examples

Using phi to represent an angle in trigonometry

sin⁡2ϕ+cos⁡2ϕ=1\sin^2 \phi + \cos^2 \phi = 1 
\sin^2 \phi + \cos^2 \phi = 1

Representing the golden ratio in mathematics

ϕ=1+52≈1.618\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618 
\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618

Using phi in physics for phase angle in oscillations

x(t)=Acos⁡(ωt+ϕ)x(t) = A\cos(\omega t + \phi) 
x(t) = A\cos(\omega t + \phi)