Digitalfox Posted November 17, 2009 Share Posted November 17, 2009 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 :) Link to comment Share on other sites More sharing options...
0 XerXis Posted November 17, 2009 Share Posted November 17, 2009 (edited) 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 Link to comment Share on other sites More sharing options...
0 Digitalfox Posted November 17, 2009 Author Share Posted November 17, 2009 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 :) Link to comment Share on other sites More sharing options...
0 XerXis Posted November 17, 2009 Share Posted November 17, 2009 (edited) 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 Link to comment Share on other sites More sharing options...
0 Digitalfox Posted November 17, 2009 Author Share Posted November 17, 2009 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 :) Link to comment Share on other sites More sharing options...
0 XerXis Posted November 17, 2009 Share Posted November 17, 2009 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 Link to comment Share on other sites More sharing options...
0 Digitalfox Posted November 17, 2009 Author Share Posted November 17, 2009 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? Link to comment Share on other sites More sharing options...
0 XerXis Posted November 17, 2009 Share Posted November 17, 2009 (edited) 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 Link to comment Share on other sites More sharing options...
0 Digitalfox Posted November 20, 2009 Author Share Posted November 20, 2009 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 Link to comment Share on other sites More sharing options...
0 bdsams Veteran Posted November 20, 2009 Veteran Share Posted November 20, 2009 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? Link to comment Share on other sites More sharing options...
0 Digitalfox Posted November 20, 2009 Author Share Posted November 20, 2009 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 Link to comment Share on other sites More sharing options...
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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 ):
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 :)
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