Results 1 to 13 of 13

Thread: Any Maths wizards in the house?

  1. #1
    Member
    Join Date
    Aug 2015
    Posts
    79
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0

    Any Maths wizards in the house?

    Im helping my son with some engineering maths at home before he starts his course. (when i say help i basically try to learn it then teach him as I suck at maths)

    cosh^2(x)+5sinh(x)+6=1+sinh^2(x)
    Solve for x

    Trying to have a go at this altho Im struggling. From using microsoft maths it shows the answer as x = 0.864726118559. But I cant seem to get to that answer. Any help would be much appreciated!

    0 Not allowed! Not allowed!

  2. #2
    Old Timer J M Fahey's Avatar
    Join Date
    Oct 2007
    Location
    Buenos Aires, Argentina
    Posts
    10,290
    Thumbs Up/Down
    Received: 347/5
    Given: 356/5
    My Calculus is very rusty, learnt it 48 years ago an slowly lost it, same as German and Russian languages, for lack of everyday use.
    But in any case: neither MM nor any other software will help him, except as an after the fact results checker.
    "A number" is NOT enough, even if accurate, Teachers want him to go through all the hoops and explain them how he reached the result.

    0 Not allowed! Not allowed!
    Juan Manuel Fahey

  3. #3
    Member
    Join Date
    Aug 2015
    Posts
    79
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Yeah thats it, Im trying to do the working out however i keep getting it wrong, so im wondering if anyone on here could figure it out. Maybe i should go back to school ha!

    0 Not allowed! Not allowed!

  4. #4
    Lifetime Member Enzo's Avatar
    Join Date
    May 2006
    Location
    Lansing, Michigan, USA
    Posts
    30,433
    Thumbs Up/Down
    Received: 446/1
    Given: 0/0
    Read his text.


    I was a physics major in college, took all the calculus and other math, had the algebra and trig and such in high school. I remember liking diffy-Q (differential equations), but don;t remember a thing about it. College was over 50 years ago. Never used the stuff once I left college. Wish I could help.

    0 Not allowed! Not allowed!
    Education is what you're left with after you have forgotten what you have learned.

  5. #5
    Senior Member SoulFetish's Avatar
    Join Date
    Jan 2016
    Location
    Massachusetts
    Posts
    717
    Thumbs Up/Down
    Received: 61/1
    Given: 33/0
    For what it's worth, you (or he) might find this book helpful:


    From the Preface:
    "Quick Calculus should teach you the elementary techniques of differential and integral calculus with a minimum of wasted effort on your part; it is designed for you to study by yourself Since the best way for anyone to learn calculus is to work problems, we have included many problems in this book. You will always see the solution to your problem as soon as you have finished it, and what you do next will depend on your answer. A correct answer generally sends you to new material, while an incorrect answer sends you to further explana*tions and perhaps another problem."

    0 Not allowed! Not allowed!
    If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

  6. #6
    Supporting Member The Dude's Avatar
    Join Date
    May 2010
    Location
    Sioux Falls, SD
    Posts
    5,212
    Thumbs Up/Down
    Received: 193/0
    Given: 159/0
    Quote Originally Posted by Off-Beat View Post
    ...... cosh^2(x)+5sinh(x)+6=1+sinh^2(x)......
    Looks like authentic frontier gibberish to me.

    0 Not allowed! Not allowed!
    “Yeah, well, you know, that’s just, like, your opinion, man.”

  7. #7
    Senior Member
    Join Date
    Jul 2017
    Location
    British Columbia
    Posts
    357
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Quote Originally Posted by Off-Beat View Post
    cosh^2(x)+5sinh(x)+6=1+sinh^2(x)
    Solve for x
    There is actually no need for calculus to solve this, you just need a little algebra, and a couple of mathematical identities connecting hyperbolic trigonometric functions.

    Here we go:

    Step 1) Bring sinh^2(x) to left side, move +6 to right side:

    => [cosh^2(x) - sinh^2(x)] + 5 sinh(x) = 1-6

    The term in square brackets is equal to 1 (this is a mathematical identity, [cosh^2(x) - sinh^2(x)] = 1, see here: https://brilliant.org/wiki/hyperboli...ric-functions/ )

    So now we have:

    1 + 5 sinh(x) = -5


    Step 2) Move the +1 to the right hand side
    => 5 sinh(x) = -5-1

    => 5 sinh(x) = -6


    Step 3) Divide both sides by 5

    => sinh(x) = -6/5

    => sinh(x) = -1.2

    Sinh(x) is a well-behaved function, and therefore has a well-defined inverse function. So all we have to do operate on both sides of this last equation with sinh-1(x).

    Step 4) Take sinh-1() of both sides:

    sinh-1[sinh(x)] = sinh-1(-1.2)

    By definition of the inverse function, the left hand side of the equation is now just (x), so we have the result we want:

    Step 5: x = sinh-1(-1.2)


    If I was your son's teacher, I would happily accept this answer and give him full marks, but just in case his actual teacher wants a numerical answer, we can take this a little further.

    Step 6: The sinh-1(x) function can be written explicitly as ( see Hyperbolic Functions: Inverses ):

    sinh-1(x) = ln[x + square_root(x2 + 1)]

    (This forum doesn't seem to support a square-root sign, so I wrote "square_root"; and "ln" is the natural log, i.e. log to the base "e")

    So we can now use this form of sinh-1(x) to evaluate the equation we found in step 5:

    x = ln{-1.2 + square_root[(-1.2)2 + 1]}

    Everything on the right hand side can be found with an ordinary scientific calculator (or the Internet). Solving, I get:

    x = -1.015973134

    Hope that helps!

    -Gnobuddy

    P.S. I don't get the same answer as Microsoft Maths, so your son still has some detective work to do. If I made an algebra mistake, maybe he can find and fix it. But he should be able to follow the same solution method I used.

    0 Not allowed! Not allowed!

  8. #8
    Senior Member SoulFetish's Avatar
    Join Date
    Jan 2016
    Location
    Massachusetts
    Posts
    717
    Thumbs Up/Down
    Received: 61/1
    Given: 33/0
    Quote Originally Posted by Gnobuddy View Post

    ...a couple of mathematical identities connecting hyperbolic trigonometric functions.
    .
    Took the words right out of my mouth.

    What I want to know is, and how did you format the text To display postscripts & subscripts?

    0 Not allowed! Not allowed!
    If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

  9. #9
    Senior Member
    Join Date
    Jul 2017
    Location
    British Columbia
    Posts
    357
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Quote Originally Posted by SoulFetish View Post
    What I want to know is, and how did you format the text To display postscripts & subscripts?
    If you click the "Quote" and then "Go Advanced" buttons, you get little icons that let you turn a bit of highlighted text into a subscript or a superscript (see attached screen capture). I didn't know they were there until last night, either!

    -Gnobuddy
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

Name:	subscripts_superscripts.png 
Views:	45 
Size:	29.1 KB 
ID:	47089  

    0 Not allowed! Not allowed!

  10. #10
    Supporting Member Steve A.'s Avatar
    Join Date
    May 2006
    Posts
    4,503
    Thumbs Up/Down
    Received: 110/0
    Given: 77/0
    Quote Originally Posted by Gnobuddy View Post
    There is actually no need for calculus to solve this, you just need a little algebra, and a couple of mathematical identities connecting hyperbolic trigonometric functions.
    I would trust your work more than Microsoft Maths whatever that may be. I would imagine that a decent scientific calculator would be able to handle most if not all of the computations.

    FWIW I was just looking at calculator apps yesterday and found some that can emulate "real" calculators from HP or TI although you do need to download the ROM from an actual calculator as THAT is protected by copyrights (the emulators are perfectly legal.) On a 7 or 8 inch tablet those emulators should really rock!

    Steve A.

    EDIT here is a full-size image of the screen capture you posted on subscripts and superscripts... Thanks for educating us!



    P.S. I found those two options after pressing "Go Advanced"...

    0 Not allowed! Not allowed!
    Last edited by Steve A.; 02-15-2018 at 08:19 PM.

  11. #11
    Senior Member
    Join Date
    Jul 2017
    Location
    British Columbia
    Posts
    357
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Quote Originally Posted by Steve A. View Post
    I would trust your work more than Microsoft Maths
    Well, I trust Microsoft about as far as I could throw the proverbial elephant.

    But I didn't check my answer (easy enough to do, simply back-substitute the number I got into the original equation, online, or with a calculator that does include hyperbolic trig functions.) So it's always possible I made a mistake.

    Quote Originally Posted by Steve A. View Post
    I would imagine that a decent scientific calculator would be able to handle most if not all of the computations.
    My trusty old Casio fx260 Solar doesn't include any hyperbolic trig functions, but I wouldn't be surprised if some newer and more powerful calculators do. Sharp has some very nice engineering-oriented calculators that have become standards in many university engineering courses here in British Columbia.

    The web link I included in my answer lets you evaluate sinh-1(x) using log, square, and square root functions, which even the most basic scientific calculators do have.

    -Gnobuddy

    0 Not allowed! Not allowed!

  12. #12
    Senior Member potatofarmer's Avatar
    Join Date
    Feb 2013
    Posts
    359
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Wolfram Alpha makes for a pretty great answer check too: https://www.wolframalpha.com/

    https://www.wolframalpha.com/input/?...1%2Bsinh%5E2(x)

    0 Not allowed! Not allowed!

  13. #13
    Senior Member
    Join Date
    Jul 2017
    Location
    British Columbia
    Posts
    357
    Thumbs Up/Down
    Received: 0/0
    Given: 0/0
    Quote Originally Posted by potatofarmer View Post
    Wolfram Alpha makes for a pretty great answer check too: https://www.wolframalpha.com/
    Thanks for the reminder!

    I've used Alpha before. I also remember when it was new, and Stephen Wolfram published a book that more or less claimed that his new software basically made every other mathematical approach ever used on earth obsolete and worthless.

    Wolfram's hyperbole aside, it is a great tool. And it seems Wolfram Alpha agrees with my step 5 equation (screenshot attached.)

    -Gnobuddy
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

Name:	hyperbolic_trig_equation_Screenshot_2018-02-15_21-21-34.png 
Views:	15 
Size:	12.4 KB 
ID:	47157  

    0 Not allowed! Not allowed!

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Replies: 1
    Last Post: 09-07-2017, 06:23 AM
  2. Any speaker gurus in the house?
    By spsimmons in forum Music Electronics
    Replies: 23
    Last Post: 03-07-2015, 07:57 PM
  3. Leesona 102B In The House!
    By JGundry in forum Tools and Coil Winding Gear
    Replies: 7
    Last Post: 11-16-2012, 04:54 AM
  4. House of Fire Article
    By gbono in forum Maintenance, Troubleshooting & Repair
    Replies: 0
    Last Post: 11-30-2011, 09:42 PM
  5. Phase splitter/inverter maths/calculations!
    By slideman82 in forum Theory & Design
    Replies: 23
    Last Post: 11-06-2007, 04:46 PM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •