How to use theta(θ), var theta(𝜗) and big theta(Θ) symbol in LaTeX?

In mathematical notation, theta (θ) symbols play a crucial role in representing angles and variables. This article explores the use of small theta (θ), variant theta (𝜗), and big theta (Θ) symbols in LaTeX.

Use of small theta like θ

Small theta (θ) is commonly used to represent angles in mathematical expressions. In LaTeX, you can include \theta command for inline and display mode.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
 \noindent If we want to express the Cartesian coordinates in terms of polar coordinates, we might write $ x=r\cos⁡(\theta) \; \mbox{and} \; y=r\sin(\theta)$, where $\theta$ represents the angle.
 \[\theta^\circ = \,angel ,\quad x= r\sin\theta, \quad y=r\sin\theta\]
 \[z=re^{i\theta},\quad f(\theta+2k\pi)=g(\theta),\quad e^{\theta}=\frac{1}{r} \frac{d}{d\theta}\]
 \[\frac{du}{d\theta} = r\left(\frac{du}{dx}\cos\theta+\frac{du}{dy}\sin\theta \right) \]
 \[\sum_{i=1}^r\frac{1}{2}r(\theta_i)^2\Delta\theta,\quad \frac{d\vec{r}}{d\theta}= \frac{dr}{d\theta}\hat{e}_{r}+r\hat{e}_{\theta}\]
 \[\begin{pmatrix} 0 & -d\theta \\ d\theta & 0 \end{pmatrix} \left|\frac{\partial r}{\partial \theta}\right| =r\]
\end{document}

Output :

Use a very simple command is theta.

Use of var theta like 𝜗

Variant theta (ϑ) is a specialized form of theta that can be employed for distinct purposes. For this, use \vartheta command.

\documentclass{article}
\begin{document}
 \noindent Let's consider a scenario where the theta function involves a parameter $\vartheta$ that encapsulates specific properties of the system under consideration. \\
 \noindent For instance, in a mathematical model describing the behavior of a dynamic system, we might encounter an equation like $\Theta(t)=A\cos(\omega t + \vartheta)$ , where $\vartheta$ represents a phase angle.
 \[\vartheta \quad \vartheta(x,y)\quad \vartheta(t)\quad\] 
 \[\vartheta_{00}(x;y)=\vartheta(x;y)\] 
 \[ \lim_{q \to 0}\frac{\vartheta(\theta/q)}{\sum{q^{1/4}}}= \cos(\pi\theta)\]
\end{document}

Output :

Equation of vartheta is represented by latex.

Big theta in latex like Θ

Big theta (Θ) notation is frequently utilized in computer science to describe the time complexity of algorithms. It represents the upper and lower bounds of the growth rate. In LaTeX, use \Theta command for this symbol.

\documentclass[11pt]{article}
\begin{document}
 \noindent The big theta notation $\Theta$ plays a pivotal role in characterizing the growth rate of algorithms. For example, if an algorithm exhibits a quadratic growth rate, we can succinctly express its time complexity as $T(n)=\Theta(n^2)$. 
 \[ f(n)=\Theta\left(g(n)\right) \quad,\quad \Theta\left(f(n)\right) \]
 \[\Theta(2n) \qquad \Theta(1) \qquad \Theta\left(n\log\left(\frac{2n}{k}\right)\right)\]
 \[ \Theta\left( 1 + \frac{n}{2}\right) \qquad\Theta(c^n) \]
\end{document}

Output :

Various expressions of algorithm are shown where Big Theta is used.

Use bold style

In this case, we will use \mathbf command. But, this command cannot change shape of symbol. It would be correct to use \boldsymbol command instead of \mathbf.

\documentclass{article}
\usepackage{amsmath}
\usepackage{bm} % for bold math symbols
\begin{document}
 \begin*{align}
    f(\bm{\theta}) &= \bm{\theta}^T \bm{X} + b \\
    &= \theta_0 x_0 + \theta_1 x_1 + \theta_2 x_2 + \ldots + \theta_n x_n + b \\
    &= \sum_{i=0}^{n} \boldsymbol{\theta}_i x_i + b
 \end*{align}
\end{document}

Output :

Although mathbf makes text bold. But, cannot convert symbols to bold format. For this, bm and boldsymbol commands are used.

Dot theta and hat theta symbol

In LaTeX, you can create symbols with dots or hats(caps) above them using the \dot{arg} and \hat{arg} commands.

\documentclass{article}
\begin{document}
  \[\dot{\theta}\quad \ddot{\theta}(r)\]
  \[\vartheta(\vec{r}\,)=r\sin(\theta)\hat{\theta}\]
  \[\dot{\theta}(x)=r\cos(\theta)\hat{\theta}\]
\end{document}

Output :

Derivative dot and hat are added to this symbol.

Conclusion

The default variant is used in this tutorial. You can take help of external package if you want. In which there are various commands to represent theta symbols.

Share tutorial

Don't forget to share if I have added any value to your education life. See you again in another tutorial. thank you!

Facebook iconTwitter iconWhatsapp iconPinterest icon

Md Jidan Mondal

LaTeX expert with over 10 years of experience in document preparation and typesetting. Specializes in creating professional documents, reports, and presentations using LaTeX.

Leave a Comment

Your email address will not be published. Required fields are marked *