Seno hiperbólico

O seno hiperbólico é uma função hiperbólica com a propriedade de gerar uma hipérbole. Sua fórmula é apresentada abaixo:^[1]

$\operatorname {senh} (t)={\frac {e^{t}-e^{-t}}{2}}$

Estendendo-se o conceito de seno para o corpo dos números complexos através da série de Taylor, verificam-se as seguintes equivalências:^[^{carece de fontes?]}

$\operatorname {senh} (t)=-i\operatorname {sen}(it)$ $\operatorname {senh} (it)=i\operatorname {sen}(t)$

Onde $i$ é a unidade imaginária.^[2]

A derivada do seno hiperbólico é o cosseno hiperbólico, assim como sua integral:^[3]

${\frac {d}{dt}}\operatorname {senh} (t)=\cosh(t)$

$\int _{}^{}\operatorname {senh} (t)dt=\cosh(t)+C$

Referências

↑ «Funções trigonométricas hiperbólicas». e-scola. Consultado em 12 de julho de 2019
↑ «Variáveis complexas». UEL. Consultado em 12 de julho de 2019
↑ Vasconcelos, Jerry Gleison Salgueiro Fidanza (2013). «FUNÇÕES HIPERBÓLICAS: HISTÓRIA, CONCEITO E APLICAÇÃO» (PDF). UFAM. p. 36-38. Consultado em 12 de julho de 2019

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Tipos	Analítica • Bijetora • Convexa • Divisor • Elementar • Exponencial • Fatorial • Identidade • Inclusão • Inteira • Inversa • Iterada • Limitada • Integral de Tchebychev • Logaritmo • Logaritmo natural • Monótona • Parcial • Polinomial • Retangular • Simples • Sinal • Sobrejetora • Suave
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Hiperbólicas	Seno hiperbólico • Cosseno hiperbólico • Tangente hiperbólica • Cotangente hiperbólica • Secante hiperbólica • Cossecante hiperbólica
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