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What is the difference?

  1. Sep 7, 2007 #1
    There are SIN and SINH. The first one is familiar as SINUS on calculus (or trigonometry), but, I don’t know what SINH means. Can anybody here explain me what is meant by “H” letter on the SINH? Please advance
  2. jcsd
  3. Sep 7, 2007 #2


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  4. Sep 7, 2007 #3


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    It's Hyperbolic Sine. The H is abbreviated for Hyperbolic. you can read it up here.

    [tex]\sinh x = \frac{e ^ {x} - e ^ {-x}}{2}[/tex]

    [tex]\cosh x = \frac{e ^ {x} + e ^ {-x}}{2}[/tex]

    [tex]\tanh x = \frac{\sinh x}{\cosh x} = \frac{e ^ {x} - e ^ {-x}}{e ^ {x} + e ^ {-x}}[/tex]

    [tex]\coth x = \frac{\cosh x}{\sinh x} = \frac{e ^ {x} + e ^ {-x}}{e ^ {x} - e ^ {-x}}[/tex]
  5. Sep 7, 2007 #4
    Thank you.
  6. Sep 7, 2007 #5


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    circular functions and hyperbolic functions.

    given any curve f and a fixed point on it and a direction, you get two functions. i.e. given input t, go along the curve a distance t, then look at the x and y coordinates x(t) = cosf(t) and y(t) = sinf(t).
  7. Sep 7, 2007 #6
    another way to think of it is

    cosh(ix) = cos(x)
    sinh(ix) = i*sin(x)
  8. Sep 7, 2007 #7


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    Just to add to this list:
    The "fundamental solutions" to the differential equation y"+ y= 0 are cos(x) and
    sin(x). "Fundamental" because if y is a solution to y"+ y= 0, satifying y(0)= A, y'(0)= B, then y(x)= A cos(x)+ B sin(x).

    The fundamental solutions to the differential equation y"- y= 0 are cosh(x) and sinh(x). If y is a solution to y"- y= 0 satisfying y(0)= A, y'(0)= B, then y(x)= A cosh(x)+ B sinh(x).
    Normally, the general solution to y"- y= 0 is written C1[/sup]ex+ C2 e-x but that is harder to evaluate at x= 0.
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