What is the difference between SIN and SINH?

[tomcenjerrym]

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

 

[cristo]

The first function is the sine function: http://mathworld.wolfram.com/Sine.html. The second, sinh, is the hyperbolic sine function: http://mathworld.wolfram.com/HyperbolicSine.html

 

[VietDao29]

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

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

$$\sinh x = \frac{e ^ {x} - e ^ {-x}}{2}$$

$$\cosh x = \frac{e ^ {x} + e ^ {-x}}{2}$$

$$\tanh x = \frac{\sinh x}{\cosh x} = \frac{e ^ {x} - e ^ {-x}}{e ^ {x} + e ^ {-x}}$$

$$\coth x = \frac{\cosh x}{\sinh x} = \frac{e ^ {x} + e ^ {-x}}{e ^ {x} - e ^ {-x}}$$

 

[tomcenjerrym]

Thank you.

 

[mathwonk]

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).

 

[JonF]

another way to think of it is

cosh(ix) = cos(x)
sinh(ix) = i*sin(x)

 

[HallsofIvy]

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 C_{1[/sup]e^x+ C2 e^-x but that is harder to evaluate at x= 0.}