# arc x and Arc x

• Jun 10th 2010, 02:27 PM
Noraowolf1
arc 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 PM
Sudharaka
Quote:

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.
• Jun 12th 2010, 12:22 PM
Soroban
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.