Is Sin^-1 X = (Sin X ) ^ -1 ?from my book it stated :f(x) =

1. Nov 30, 2011

Voilstone

Is Sin^-1 X = (Sin X ) ^ -1 ??from my book ... it stated :f(x) =

Is Sin^-1 X = (Sin X ) ^ -1 ??

from my book ... it stated :
f(x) = Sin ^-1 X
f'(x) = 1/(1-X^2)^1/2

instead of f'(x) = -cot X / sin X

Why is it so ???

2. Nov 30, 2011

DivisionByZro

Re: Derivative

First of all, sin^1(x) =/= 1/(sinx). It's a convention to write it as sin^1(x), but it means arcsin of x, the inverse function of sinx.

Do you know how to take the derivative of inverse trigonometric functions? This is typically covered in any freshman calculus book. Try to see if you can't come up with the answer on your own first, we don't want to rob you of the spirit of discovery. :

3. Dec 1, 2011

Voilstone

Re: Derivative

thanks !!! wanna make sure between the relationship with sin X and Sin ^-1 X ..... =D

4. Dec 1, 2011

dextercioby

Re: Derivative

It's higly misleading esecially to starters not to use <arcsin> for the inverse of sine. But this unfortunate notation with the -1 in the exponent is propagated also because of software such as maple and mathematica and essentially should stay there and not invade calculus textbooks...

5. Dec 1, 2011

Staff: Mentor

Re: Derivative

I agree that inverse trig functions should first be presented as arcsin, arccos, arctan, etc., rather that sin-1, cos-1, tan-1. However, how can we represent the inverse of an arbitrary function f other than with the standard notation f-1?

The problem is that students confuse expressions such as x-1, the multiplicative inverse of x (or 1/x), with f-1, the function inverse of f, which has nothing to do with multiplication or division.

Exponent notation for function inverses is a convenient and compact form that, like all notations, takes some time to learn.

6. Dec 1, 2011

Voilstone

Re: Derivative

agree with that ... when i tell some of my frens that Sin^-1 X =/= 1/Sin X , they feel shock too ....