What Is Cosh X

Similarly we define the other inverse hyperbolic functions.

What is cosh x. The inverse hyperbolic functions are multiple valued and as in the case of inverse trigonometric functions we restrict ourselves to principal values for which they can be considered as single valued. Use definition of cosh. Cosh x dx sinh x c.

Therefore d cosh x dx e x e x 2 sinh x. Cosh x has its minimum value of 1 for x 0 and tends to infinity as x tends to plus or minus infinity. Cosh x e x e x 2.

Cosh x e x e x 2 pronounced cosh they use the natural exponential function e x. The hyperbolic cosine function. One can verify this result using the definitions cosh x e x e x 2 and sinh x e x e x 2.

The derivative of e x with respect to x is e x. The graph of the function a cosh x a is the catenary the curve formed by a uniform flexible chain hanging freely between two fixed points under uniform gravity. Sinh x is zero for x 0 and tends to infinity as x tends to infinity and to minus infinity as x tends to minus infinity.

If x sinh y then y sinh 1 a is called the inverse hyperbolic sine of x. The decomposition of the exponential function in its even and odd parts gives the identities. Tanh x is zero for x 0 and tends to 1 as x tends to infinity and to 1 as x tends to minus infinity.

Add graph addition formulae. Cosh x dx e x e x 2. Cosh x ex e x 2.