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I'm studying in-depth complex numbers and analysis and when I'm working through certain theory, I like to refer to as many textbooks as possible.

I've always known to write mod-arg form as $r(\cos\theta + i\sin\theta)$

However, this book by J. Coroneos writes mod-arg form simplistically as $r\operatorname{cis}\theta$. In the other 7 textbooks I have referred to, I haven't come across this.

Is this is universally accepted? If I use this, will I be technically wrong or is this dude just simplifying things to make things easier.

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    https://en.wikipedia.org/wiki/Cis_(mathematics) – 2017-01-15
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    It's just their convention. Some texts use that (and so do I sometimes). It's also shorthand for $r e^{i\theta}$. You're okay. – 2017-01-15
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    Which one should I use though? – 2017-01-15
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    Whatever what you want – 2017-01-15
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    $cis(t)$ is useless notation, because it gets replaced by $e^{it}$ immediately. I recommend getting used to the exponential form. – 2017-01-15
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    I think "cis" is teddy-bear for beginners. I guess most people will know what you mean when you write it, but when doing any kind of calculation, $e^{it}$ works better. – 2017-01-15
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    @Kaynex : It is not useless: It is good to avoid writing it in the form of an exponential function when the fact that it's an exponential function is just what you're trying to prove. – 2017-01-15
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    Proper notation is $r\sin\theta,$ not $rsin\theta$; it's coded as r\sin\theta. The effect is not only de-italicize $\sin$ but also proper spacing in expressions like $a\sin b$ and $a\sin(b)$. Note that there is less space to the right of $\sin$ in $a\sin(b)$ than in $a\sin b$; the spacing depends on the context. The sequence \cis is not a standard control sequence, so you can write \operatorname{cis}\theta and you'll see $\operatorname{cis}\theta. \qquad$ – 2017-01-15

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It's somewhat standard, but mathematicians generally prefer writing $e^{i\theta}$ to writing $\operatorname{cis}\theta.$

The "$\operatorname{cis}$" notation is useful when you want to avoid writing it in the form of an exponential function because the fact that $\theta\mapsto\cos\theta+i\sin\theta$ is an exponential function is just what you're trying to prove.