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The relationship between hyperbolic and circular functions

  1. Sep 27, 2009 #1
    Hello!
    A book on calculus was introducing hyperbolic functions and pointed out that the identities such as cosh x and sinh x, etc. for hyperbolic functions were analogous to cos x and sin x for circular functions. I tried finding some internet sources explaining why this is so, but they tend to be overly complicated or unsatisfactory. Could someone point me in the direction of any recommended sources; or, perhaps, offer a brief explanation (presumably the explanation is not so brief!…)
    Thanks in advance.
     
  2. jcsd
  3. Sep 27, 2009 #2

    lurflurf

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    Circular functions are parametritizations of the equation
    x^2+y^2=1
    Hyperbolic functions are parametritizations of the equation
    y^2-x^2=1
    so that explains the anaology
    futher if complex numbers are used we see hyperbolas and circles as equivelent in some sense
     
  4. Sep 28, 2009 #3
    Thanks ever so much lurflurf.
    Because for any trig identities, apparently you simply substitute in the hyperbolic equivalent, changing the sign for a product of two sins. Is this simply a consequence of the minus sign in the above equation, and that the others remain 'unaffected'?
     
  5. Sep 29, 2009 #4

    lurflurf

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