In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle …

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch Definition of hyperbolic functions Hyperbolic sine of x \displaystyle \text {sinh}\ x = \frac {e^ {x} - e^ {-x}} {2} sinh x = 2ex −e−x …

Relations to Trigonometric Functions sinh (z) = -i sin (iz) csch (z) = i csc (iz) cosh (z) = cos (iz) sech (z) = sec (iz) tanh (z) = -i tan (iz) coth (z) = i cot (iz)

Learn Hyperbolic Trig Identities and other Trigonometric Identities, Trigonometric functions, and much more for free. Download Hyperbolic Trig Worksheets.

Both cosh and sech are Even Functions, the rest are Odd Functions. The Derivatives are: d dx sinh (x) = cosh (x) d dx cosh (x) = sinh (x) d dx tanh (x) = 1 − tanh 2 (x) Math explained in easy language, plus puzzles, games, quizzes, worksheets and a …

三角函数有反三角函数，就是三角函数的逆函数，双曲函数也有，下面是sinh、cosh、tanh的反函数图像： 并且我们是可以求出各个反双曲函数的对数表示式的： 这些是怎么算出来的？ 其实和我们之前计算反函数是一样的，以sinh的反函数为例： 说白了就是解方程，所以其他的反函数函数的对数表示式我们也都是可以计算出来的，大家可以试一下。 OK，今天介绍双曲函数就到这里，其他内容后续再来分享吧。 如果大家上完课、看完这篇内容还有疑问可以私信我，毕竟Further …

在 数学 中， 双曲函数 是一类与常见的 三角函数 （也叫圆函数）类似的函数。 最基本的双曲函数是 雙曲正弦 函数 和 雙曲餘弦 函数 ，从它们可以导出 双曲正切 函数 等，其推导也类似于三角函数的推导。 双曲函数的反函数称为 反双曲函数。 双曲函数的定义域是实数，其自变量的值叫做 双曲角。 双曲函数出现于某些重要的线性 微分方程 的解中，譬如說定义 悬链线 和 拉普拉斯方程。 最簡單的幾種雙曲函數為 [1]： {\displaystyle \tanh x= {\frac {\sinh x} {\cosh x}}= {\frac {e^ {x} …

Bài này sẽ nêu các công thức xác định sinh x, cosh x, tanh x, coth x, sech x, csch x và một số tính chất cơ bản liên quan. sinh, cosh, tan...

The other hyperbolic functions tanh x, coth x, sech x, csch x are obtained from sinh x and cosh x in exactly the same way as the trigonometric functions tan x, cot x, sec x and csc x are defined in terms of sin x and cos x: The derivatives of hyperbolic functions can be easily found as these functions are defined in terms of exponential functions.

Taylor series expansions of hyperbolic functions, i.e., sinh, cosh, tanh, coth, sech, and csch.