双曲函数与反双曲函数的一些公式 - 知乎 - 知乎专栏
1、双曲正弦. \sinh x = \frac {e^ {x} - e^ {-x}} {2} \\. 2、双曲余弦. \cosh x = \frac {e^ {x} + e^ {-x}} {2} \\. 3、双曲正切. \sinh x =\frac {\sinh} {\cosh} = \frac {e^ {x} - e^ {-x}} {e^ {x} + e^ {-x}} \\. 4、双曲余切. \coth x = \frac {\cosh x} {\sinh x} =\frac {e^ {x} + e^ {-x}} {e^ {x} - e^ {-x}} \\. 5、双曲正割.
sinh^2 x + cosh^2 x - Wolfram|Alpha
Definite integral mean square. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….
双曲函数 - 维基百科，自由的百科全书
這裡以自然對數即雙曲角作為參數的函數，是自然對數的逆函數指數函數，即要形成指定雙曲角 ，在漸近線即x或y軸上需要有的 或 的值。 顯見這裡的底邊是 ( e u + e − u ) 2 2 {\displaystyle \left(e^{u}+e^{-u}\right){\frac {\sqrt {2}}{2}}} ，垂線是 ( e u − e − u ) 2 2 {\displaystyle ...
Hyperbolic Trigonomic Identities - Math2.org
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)
Prove that sinh (2x) = 2sinh (x)cosh (x) - Mathematics Stack …
2019年12月26日 · Prove that $$sinh(2x) = 2sinh(x)cosh(x)$$ My (wrong) solution: $$sinh(x) = \frac{e^x - e^{-x}}{2}$$ $$sinh(2x) = \frac{e^{2x} - e^{-2x}}{2}$$ $$sinh(2x) = \frac{(e^{x} + e^{-x})(e^{x} - e^{-x})}{2}$$ $$sinh(2x) = cosh(x)sinh(x)$$
Hyperbolic Functions - Math is Fun
Hyperbolic Sine: sinh (x) = ex − e-x 2. (pronounced "shine") Hyperbolic Cosine: cosh (x) = ex + e-x 2. (pronounced "cosh") They use the natural exponential function ex. And are not the same as sin (x) and cos (x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary.
双曲函数 - 数学乐
双曲函数. 这是最常见的三个双曲函数：. sinh 、 cosh 和 tanh. （就是双曲正弦、双曲余弦和双曲正切）. sinh x = ex − e−x 2. cosh x = ex + e−x 2.
6.9 Calculus of the Hyperbolic Functions - OpenStax
There are a lot of similarities, but differences as well. For example, the derivatives of the sine functions match: (d/dx)sinx=cosx(d/dx)sinx=cosxand (d/dx)sinhx=coshx. (d/dx)sinhx=coshx. The derivatives of the cosine functions, however, differ in sign: (d/dx)cosx=−sinx,(d/dx)cosx=−sinx,but (d/dx)coshx=sinhx.
Calculate cosh (x) given sinh (x) - Mathematics Stack Exchange
2014年7月15日 · Using $\cosh^2x-\sinh^2x=1$ you can evaluate it. But unlike circular trig functions, there is only a single value for $ \cosh( \sinh^{-1}(x)) $
Cosh Calculator | Hyperbolic Cosine Function
2024年7月23日 · Use the identity cosh 2 x − sinh 2 x = 1 along with the fact that sinh is an odd function, which implies sinh(0) = 0. Read the answer from the graph of the hyperbolic cosine function. Use an online cosh calculator .