# What is the difference between arcsin and inverse sin?

1. Dec 23, 2004

### tony873004

What's the difference between arcsin and inverse sin?
arccos and inverse cos?
arctan and inverse tan?

2. Dec 23, 2004

### Dr Transport

nothing they are the same.....different ways of saying the same thing.

3. Dec 23, 2004

### dextercioby

None,none,none...There is a trick though.For sine and cosine for example,defined on R,the rule f:A->B,f-1:B->A would not apply,since
$$\sin x:R\rightarrow [-1,+1]$$
$$\cos x:R\rightarrow [-1,-1]$$
$$\arcsin x:[-1,+1]\rightarrow [-\frac{\pi}{2},+\frac{\pi}{2}]$$
$$\arccos x:[-1,+1]\rightarrow [0,\pi]$$
,so the 'arcsine' and 'arccosine' are the inverse functions of 'sine' respectively 'cosine',BUT SINE X is inveritble only on the interval $[-\frac{\pi}{2},+\frac{\pi}{2}]$,and similar for COSINE X.
I'll let u work out the other examples for circular trigonometric functions:tan,cotan,sec,cosec.

Daniel.