Help with math problem

Discussion in 'Community Discussion' started by Shamus, Mar 13, 2008.

  1. Shamus macrumors 6502a

    Shamus

    Joined:
    Feb 26, 2006
    #1
    Hi everyone,

    I've just started out at uni in melbourne, and am finding it great! I have been given a set of questions to get done, and i've done most of them without any problems. but i've gotten to one which has got me stuck :(, and was wondering if anyone could explain how i do it.

    The problem:
    Simplify the following expression:

    cosec^2 (x) - cot^2 (x)

    If anyone can explain it to me it would be very much appreciated, thanks guys.
     
  2. nikopolidis macrumors regular

    Joined:
    Dec 21, 2007
    #2
    It's simple if I correctly understand that cot(x) means ctg(x). If not then explain what do you mean be cot(x). If cot)x) = ctg(x) = cos(x)/sin(x) then solution of your problem is below...

    So, let's begin...

    Your problem: cosec^2(x) - cot ^2(x)
    Solution: cosec^2(x) - cot ^2(x) = 1/sin^2(x) - cos^2(x)/sin^2(x) = 1/sin^2(x) - (1-sin^2(x))/sin^2(x) = 1/sin^2(x) - 1/sin^2(x) + 1 = 1

    That's it! :)
     
  3. prostuff1 macrumors 65816

    prostuff1

    Joined:
    Jul 29, 2005
    Location:
    Don't step into the kawoosh...
    #3
    The man has the right answer and if you go to wikipedia you can find the equivalents for the trig functions.

    The only thing different i would have done with what nikopolidis showed was with the last step.

    1 - 1 + sin^2(x) = 1
    .....sin^2(x)

    You should be able to understand all the step nikopolidis made but i figured i would through my 2 cents in
     
  4. nikopolidis macrumors regular

    Joined:
    Dec 21, 2007
    #4
    Yep, thanks! Now it becomes more clear! ;)
     
  5. Melrose macrumors 604

    Melrose

    Joined:
    Dec 12, 2007
    Location:
    In a sidewalk.
    #5
    I don't mean to hijack the thread, but it is math-related: Does anyone know the formula that proves the shortest distance between two points is not a straight line? I heard of this once many years ago..
     
  6. creator2456 macrumors 68000

    creator2456

    Joined:
    Jul 10, 2007
    Location:
    Chicago
    #6
    That is hard to believe, but if it can be proven, then it must be true.

    To the OP, the answers above are correct.

    One of my favorite 'math' problems:

    girls = money x time
    time = money
    ∴ girls = money^2
    money = root of all evil
    ∴ girls = √evil^2

    girls = evil
     
  7. prostuff1 macrumors 65816

    prostuff1

    Joined:
    Jul 29, 2005
    Location:
    Don't step into the kawoosh...
    #7
    That is a very good math problem indeed... just don't let the girlfriend see it like mine did... they won't be impressed
     
  8. Gelfin macrumors 68020

    Gelfin

    Joined:
    Sep 18, 2001
    Location:
    Denver, CO
    #8
    I don't think you're going to find this because it isn't true, at least for planar Euclidean geometry. The shortest distance between two points is a straight line.

    You're probably thinking of a sphere, where the shortest distance between two points is frequently curved on the 2-manifold surface. It's relevant to navigation where the shortest route between two distant points involves following a "great circle" instead of a straight line drawn on a map.
     
  9. Melrose macrumors 604

    Melrose

    Joined:
    Dec 12, 2007
    Location:
    In a sidewalk.
    #9
    What I'm thinking of was somehow tied in with the math Albert Einstein used in showing space is curved... but that's way out of my league to say the least ;) That sphere thing you mentioned always confused me.
     
  10. iSamurai macrumors 65816

    iSamurai

    Joined:
    Nov 9, 2007
    Location:
    ɹǝpun uʍop 'ǝuɐqsı&#
    #10
    don't you just like maths? I'm also doing this.

    [​IMG]

    here's your solution to your problem:

    [​IMG]

    P.S. Images from iSight :p
     
  11. Melrose macrumors 604

    Melrose

    Joined:
    Dec 12, 2007
    Location:
    In a sidewalk.
    #11
    The funny thing is that I love math, and aced it in school. It just takes me longer than most to grasp how certain elements of it work.

    One of my favourite books is The Universe and Dr Einstein, the explanation of his theories on relativity, etc. It's a good read.

    Trig was not one of my specialities, alas... My dad (a tool and die machinist) is wonderful at it and loves it, even though he doesn't do that stuff anymore.
     

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