Using the derivative of arcsine to solve for x

[Sparky_]

Using the derivative of arcsine to solve for "x"

Greetings,

How can I use:

$$\frac {d sin^-1(x)}{dx} = \frac {1}{\sqrt{(1-x^2)}}$$

to calculate values for arc sine?

For example:

$$arcsin(x) = \int\frac {1}{\sqrt{(1-x^2)}} dx$$

How can I use equation such that I enter “0.5” in for x and turn-the-crank and this equation spits out “30 degrees” or “0.524 radians”

Just curious.

Thanks
Sparky_

 

[mathman]

What do you have in mind by "turn-the-crank"? Assuming the range of the integral is (0,x) you need some sort of integration algorithm, like Simpson's rule. The answer will be in radians.

 

[Sparky_]

Since the integral would have a range - as you said (o,x).

will I be able to enter a single number and get the arcsine of that number -

I enter x=0.5 and integrate (somehow from x= 0.5 to 0.5 though I know this would give 0 - explanation help here??) and get 0.524 radians.

If I do x= some point to some other point, would that result not be the difference ini two arcsine's?

Thanks again

 

[HallsofIvy]

Since the integral would have a range - as you said (o,x).

will I be able to enter a single number and get the arcsine of that number -

I enter x=0.5 and integrate (somehow from x= 0.5 to 0.5 though I know this would give 0 - explanation help here??) and get 0.524 radians.

No, from 0 to 0.5, not "0.5 to 0.5".

If I do x= some point to some other point, would that result not be the difference ini two arcsine's?

Yes, it would. And arcsin(0)= 0.

Thanks again

 

[Sparky_]

Mathman and HallsofIvy -

Thanks so much!

I'm going to play with this a little, I may have another question later.

I wish I had Mathcad and Mathmatica so I could "turn-the-crank" on the integration a little easier.

Does you know of any free / share ware out there that is can do some of the functions of mathcad / mathmatica.