pmatrix with \left( \frac \right)

The following MWE results in the Matrix shown in the picture. I would like the braces of the cos- and sin-functions in the first column not to touch each other. How can I achieve that?

\documentclass{scrreprt}
\usepackage{amsmath}
\usepackage{array}

\begin{document
\begin{align}
^{V}\boldsymbol{T}_{L}=
\begin{pmatrix}
cos\left(\frac{\pi\delta_i}{180}\right) & -sin\left(\frac{\pi\delta_i}{180}\right)  & 0 \\
sin\right(\frac{\pi\delta_i}{180}\left) & cos\left(\frac{\pi\delta_i}{180}\right)   & 0 \\
0                            & 0                                   & 1
\end{pmatrix}
\end{align}
\end{document}

• the easiest thing to do is add just manually add a bit of space after the first row: ... \\[3pt]. be sure not to leave any space before the [3pt], or it will get printed instead of being interpreted as a space. (amsmath checks that.) Oct 30, 2015 at 21:58

For such small fractions, I recommend just \bigl and \bigr, instead of \left and \right, which would choose \Big size that's too large. There's no need to cover all symbols in between.

You can increase the separation between rows with \\[1ex] or so.

Always use \sin and \cos for the functions; also I added bm that's recommended for \boldsymbol (and can be abbreviated in \bm). Also, I lowered the subscript by adding an empty superscript. The “prescript” is better preceded by {} (although in this case it wouldn't matter). Finally, don't use align for single equations.

\documentclass{scrreprt}
\usepackage{amsmath,bm}

\begin{document}

$${}^{V}\boldsymbol{T}^{}_{L}= \begin{pmatrix} \cos\bigl(\frac{\pi\delta_i}{180}\bigr) & -\sin\bigl(\frac{\pi\delta_i}{180}\bigr) & 0 \\[1ex] \sin\bigl(\frac{\pi\delta_i}{180}\bigr) & \cos\bigl(\frac{\pi\delta_i}{180}\bigr) & 0 \\[1ex] 0 & 0 & 1 \end{pmatrix}$$

\end{document}


• Thank you for your efforts! But now I got a couple of new questions: 1. What does the bm-package do? 2. Why not use align for single equations?
– Max
Oct 30, 2015 at 22:04
• by the way: the empty superscript thing is awesome!
– Max
Oct 30, 2015 at 22:04
• @Max For the align question, spacing and semantics, see e.g. align vs equation Oct 30, 2015 at 22:08
• @Max bm realizes \boldsymbol in a much better way. Vertical spacing is better with equation when a single formula is to be displayed. The empty superscript is an old trick that comes in handy several times: for instance if you have $a_{i}b_{i}^{2}$ the subscripts would be misaligned; with $a^{}_{}ib_{i}^{2}$ they are at the same level. Oct 30, 2015 at 22:09
• @Max In this case it's better not to touch the code; you could make an experiment, if you have time. About \tan^{-1} I have a strong opinion: never. ;-) I know that it should be interpreted as the inverse function but there are two reasons why it's wrong: (1) the tangent function is not (globally) invertible; (2) \tan^2 had been used for more than a century before the ^{-1} notation for an inverse function came into use. Similarly the arcsine is the inverse function of a suitable restriction of the sine function, so \sin^{-1} is abusive too. Oct 30, 2015 at 22:26

Since you load the array package, there is another method for slightly increasing row height of the matrix automatically. You just add \renewcommand{\arraystretch}{1.2} within your environment to increase the height by about 20%. I agree with egreg on the rest of changes he made.

\documentclass{scrreprt}
\usepackage{amsmath,bm}
\usepackage{array}
\begin{document}

\begin{align}\renewcommand{\arraystretch}{1.2}
^{V}\boldsymbol{T}^{}_{L}=
\begin{pmatrix}
\cos\bigl(\frac{\pi\delta_i}{180}\bigr) & -\sin\bigl(\frac{\pi\delta_i}{180}\bigr) & 0 \\
\sin\bigl(\frac{\pi\delta_i}{180}\bigr) & \cos\bigl(\frac{\pi\delta_i}{180}\bigr)  & 0 \\
0                                       & 0                                        & 1
\end{pmatrix}
\end{align}

\end{document}