A variant form of the Greek letter theta commonly used as a parameter or angular variable in analysis and physics.
Examples
Angular measure in trigonometry
\sin \vartheta = \frac{\text{opposite}}{\text{hypotenuse}}
Phase angle in complex analysis
z = re^{i\vartheta} = r(\cos \vartheta + i\sin \vartheta)
Temperature variable in thermodynamics
\Delta S = \int_{\vartheta_1}^{\vartheta_2} \frac{dQ}{\vartheta}