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

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- Jun 10th 2010, 02:27 PMNoraowolf1arc x and Arc x
What's the difference between a lower-cased arc x and an upper-cased Arc x? (in sinusoids)

- Jun 10th 2010, 04:58 PMSudharaka
- Jun 12th 2010, 12:22 PMSoroban
Hello, Noraowolf1!

Quote:

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

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

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

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