Math Help - arc x and Arc x

1. arc x and Arc x

What's the difference between a lower-cased arc x and an upper-cased Arc x? (in sinusoids)

2. Originally Posted by Noraowolf1
What's the difference between a lower-cased arc x and an upper-cased Arc x? (in sinusoids)
Dear Noraowolf1,

As far as I know there is no difference. Normally the inverse functions of sine, cosine, tangent, etc are written arcsin, arccos with lowercase letters.

3. Hello, Noraowolf1!

What's the difference between a lower-cased ${\color{red}\text{a}}\text{rcsin}\,x$ and an upper-cased ${\color{red}\text{A}}\text{rcsin}\,x$ ?

I was told (many years ago) that ${\color{red}\text{A}}\text{rcsin}\,x$ indicated the principal value of $x.$

. . That is: . $-\tfrac{\pi}{2} \:\le\:x\:\le\:\tfrac{\pi}{2}$

But I've met no one who uses that interpretation.
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