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

[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 ?

 

[DivisionByZro]

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. :

 

[Voilstone]

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

 

[dextercioby]

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...

 

[Mark44]

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...

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.

 

[Voilstone]

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