# What is the difference?

1. Sep 7, 2007

### 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

2. Sep 7, 2007

### cristo

Staff Emeritus
3. Sep 7, 2007

### VietDao29

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

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

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

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

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

4. Sep 7, 2007

Thank you.

5. Sep 7, 2007

### 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).

6. Sep 7, 2007

### JonF

another way to think of it is

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

7. Sep 7, 2007

### 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 C1[/sup]ex+ C2 e-x but that is harder to evaluate at x= 0.