Hyperbolic Trig Functions Math

Cosh 2 x sinh 2 x 1.

Hyperbolic trig functions math. Cosh x cos i x displaystyle cosh x cos ix hyperbolic tangent. Csch x 1 sinh x. C o t h x c o s h x s i n h x e x e x e x e x. Derivate of c o t h x is.

The hyperbolic trigonometric functions extend the notion of the parametric equations for a unit circle. Because of this these combinations are given names. The points x y cosh u sinh u for u equal to 0 1 0 2 0 3 0 4 and 0 5 are marked on the graph with a b c d and e as their labels and green lines are drawn to them from the point o or 0 0. X cos t.

As we can see hyperbolic cotangent is an odd function meaning c o t h x c o t h 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. Tanh x i tan i x. The hyperbolic trig functions.

If x sinh y then y sinh 1 a is called the inverse hyperbolic sine of x. Sinh x e x e x 2. Sinh x e x e x 2 pronounced shine hyperbolic cosine. There are six hyperbolic functions and they are defined as follows.

Tanh x sinh x cosh x. And are not the same as sin x and cos x but a little bit similar. D d x c o t h x 1 c o t h 2 x. The two basic hyperbolic functions are sinh and cosh.

Coth x 1 tanh x. X cosh a e a e a 2 y sinh a e a e a 2. Sinh x i sin i x displaystyle sinh x i sin ix hyperbolic cosine. In many physical situations combinations of ex e x and e x e x arise fairly often.

Tanh 2 x sech 2 x 1. R 0 1 1 defined with. Sech x 1 cosh x. Coth 2 x csch 2 x 1.

Y sin t y sin t y sint to the parametric equations for a hyperbola which yield the following two fundamental hyperbolic equations. Similarly we define the other inverse hyperbolic functions. Hyperbolic cotangent is a function c o t h. Cosh x e x e x 2.

The last set of functions that we re going to be looking in this chapter at are the hyperbolic functions. Hyperbolic functions may also be deduced from trigonometric functions with complex arguments.