Can you explain me how this formula works?

[Digitalfox]

Hello.

My girlfriend sister just came to me asking for help in understanding a formula she must use in university class.

Her problem is not passing the formula to code, but on how the formula works that was given..

Here is the question ( I'll try my best to translate to English ):

Calculate Hyperbolic sine sinh(x) using the formula given.

x represents the angle in Radians. The user must introduce the angle in the interval [-180,180]:

So where x I replace with the angle given by the user.

5! is a factorial meaning 5*4*3*2*1 = 120

But I'm lost how this formula actually works,, because I couldn't get it to calculate angle 3 it always gives me strange results.

How does that formula works to calculate sinh(3)?

Using online calculator sinh(3) = 10.01787492741

Thanks :)

[XerXis]

replace x with 3? Let's say you use the 5 terms you mentioned (should give you enough precision)

You get: 3 + 3^3/(1*2*3) ...

and so on, which gives you 10.01316964

Keep in mind that this formula expects the angle as a radian, not degrees

If you want more precision you have to add more terms like: x^11/(11!) + x^13/(13!)

Edited November 17, 2009 by XerXis

[Digitalfox]

replace x with 3? Let's say you use the 5 terms you mentioned (should give you enough precision)

You get: 3 + 3^3/(1*2*3) ...

and so on, which gives you

Keep in mind that this formula expects the angle as a radian, not degrees

PS: result 10.01316964

If you want more precision you have to add more terms like: x^11/(11!) + x^13/(13!)

You mean this right?

x + ( x^3/(1*2*3) ) + ( x^5/(1*2*3*4*5)) + ( x^7/(1*2*3*4*5*6*7) ) + ( x^9/(1*2*3*4*5*6*7*8*9) ) ?

Thank you for your answer :)

[XerXis]

yes :)

Following table gives you the formula for 3 with different numbers of terms, now you know how your calculator does it ;)

3 1 3 1 3 3

3 27 6 4,5 7,5

5 243 120 2,025 9,525

7 2187 5040 0,433928571 9,958928571

9 19683 362880 0,054241071 10,01316964

11 177147 39916800 0,004437906 10,01760755

13 1594323 6227020800 0,000256033 10,01786358

15 14348907 1,30767E+12 1,09728E-05 10,01787455

17 129140163 3,55687E+14 3,63072E-07 10,01787492

19 1162261467 1,21645E+17 9,55453E-09 10,01787493

21 10460353203 5,10909E+19 2,0474E-10 10,01787493

23 94143178827 2,5852E+22 3,64162E-12 10,01787493

Edited November 17, 2009 by XerXis

[Digitalfox]

yes :)

Thanks a lot I don't know how I couldn't see how easy it was..

But now I just tried inserting -180 using the expression I just posted and it gives me -5.478413264693229E14

Using this online calculator

http://www.kephyr.com/calculator/index.php...&=Calculate

It gives me sinh(-180) = -7.4469210039092E+77

Is this because of the precision you were referring to " If you want more precision you have to add more terms like: x^11/(11!) + x^13/(13!) "?

Thank you :)

[XerXis]

As said, this function requires it's input to be in radians, not degrees! Your calculator might do the conversion itself, this formula obviously does not :)

-180 degrees = -PI radians

I've included an excel sheet as attachment with the result of sinh on three different ways, have fun ;)

Sorry, can't upload an excel file here, download from: http://www.freedownloads.be/sinus_hyper.xls

[Digitalfox]

Thank you for patience, I really appreciate the help your giving :)

I study this some years ago at university, but not practicing or using this math for a couple of years made me forget a lot of it..

Again thank you very much :)

Now well I'm a little confused, because at first when I started this topic I was using 3 as an example and using that formula did work right, since the result was 10.013169642857143..

But how come if I was not using the conversion from degrees to radium when attributing 3 to x it work right?

[XerXis]

because 3 is smaller than PI and within the boundaries -PI + PI (-180 +180). The input 3 was actually a radian angle corresponding to 172 degrees

you might understand better if you look at the graph of sinus hyperbolicus:

http://en.wikipedia.org/wiki/File:Sinh_cosh_tanh.svg

Edited November 17, 2009 by XerXis

[Digitalfox]

Hi there :)

After a couple of days of not touching this, I'm at it again..

So what I'm doing is..

The user introduces say 5 degrees, I do the conversion from degrees to radians

x = 5 * 3.14 / 180

x = 0.05235988

I replace X with that number in the formula:

x + ( x^3/(1*2*3) ) + ( x^5/(1*2*3*4*5)) + ( x^7/(1*2*3*4*5*6*7) ) + ( x^9/(1*2*3*4*5*6*7*8*9) )

And it gives me a wrong result, after looking closely at your excel sheet, I still don't get what I'm doing wrong ( But I'm sure it's something really dumb I'm doing )

Thank you

[bdsams Veteran]

just as a shortcut, i beleive you can right 3*2*1 as 3! same with 7! and 9!

how do you know its wrong, what number are you looking for?

[Digitalfox]

just as a shortcut, i beleive you can right 3*2*1 as 3! same with 7! and 9!

how do you know its wrong, what number are you looking for?

Oh I know, I was trying to make as simple as possible :)

So sinh(5) = 74.203210577789

What is giving me is x = 0.08733285794807455