TeXipedia

varTheta

Represents an uppercase variant of theta, commonly used in mathematical expressions where visual distinction from the standard theta is needed.

Overview

Serves as an alternative form of the uppercase Greek letter Theta, offering a more cursive or stylized appearance that helps distinguish variables or specific mathematical quantities.

  • Popular in physics and engineering for denoting angles and rotational quantities
  • Often used in mathematical optimization and complex analysis
  • Helpful when multiple theta-like variables need to be visually distinct in the same equation
  • Particularly common in thermodynamics for representing temperature-related parameters

Examples

Using varTheta as a parameter in a probability distribution function.

P(X≤x)=1Θ∫0xt1Θ−1dtP(X \leq x) = \frac{1}{\varTheta} \int_{0}^{x} t^{\frac{1}{\varTheta}-1} dt 
P(X \leq x) = \frac{1}{\varTheta} \int_{0}^{x} t^{\frac{1}{\varTheta}-1} dt

Representing an angle in spherical coordinates.

r(Θ,ϕ)=x2+y2+z2r(\varTheta, \phi) = \sqrt{x^2 + y^2 + z^2} 
r(\varTheta, \phi) = \sqrt{x^2 + y^2 + z^2}

Denoting a rotation angle in a transformation matrix.

R(Θ)=(cos⁡Θ−sin⁡Θsin⁡Θcos⁡Θ)R(\varTheta) = \begin{pmatrix} \cos\varTheta & -\sin\varTheta \\ \sin\varTheta & \cos\varTheta \end{pmatrix} 
R(\varTheta) = \begin{pmatrix} \cos\varTheta & -\sin\varTheta \\ \sin\varTheta & \cos\varTheta \end{pmatrix}