hyperbolic sine function

Domain:

For, the scope is also.

Parity check:

Hyperbolic sine function is the odd function whose graph passes through the origin and is symmetrical about the origin. [3]。

Proved as follows:

And then what? .

Monotonicity:

Hyperbolic sine function monotonically increases in the interval.

Hyperbolic cosine function:

Parity check:

Hyperbolic cosine function is an even function in the definition domain.

Monotonicity:

Hyperbolic cosine function y=cosh x, in the interval (-∞, 0)? It is monotonically decreasing and monotonically increasing in the interval (0, +∞). Cosh 0= 1 is the minimum value of this function.

The domain of hyperbolic cosine function is (-∞,+∞). The range is [1, +∞).

Extended data:

Hyperbolic sine function is a kind of hyperbolic function. Hyperbolic sine function is generally recorded as sinh in mathematical language, and can also be abbreviated as sh. Like trigonometric functions, hyperbolic functions are divided into six types: hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant and hyperbolic cotangent. Hyperbolic sine function and hyperbolic cosine function are two basic hyperbolic functions, from which hyperbolic tangent function can be derived.

The definition of hyperbolic sine function is: sinh = [e x-e (-x)]/2.

Hyperbolic cosine function is a kind of hyperbolic function. We know that trigonometric functions are divided into sine sin, cosine cos, tangent tan, cotangent cot, secant sec and cotangent csc. Then, similarly, hyperbolic functions can be divided into six types: hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant and hyperbolic cotangent. Hyperbolic cosine function is one of them. Hyperbolic cosine function wrote cosh or ch for short.

References:

Hyperbolic Sine Function-Baidu Encyclopedia hyperbolic cosine function-Baidu Encyclopedia