A value of $\sinh x$ or $\cosh x$ is given. Use the definitions and the identity $\cosh ^ { 2 } x - \sinh ^ { 2 } x = 1$ to find the value of the other indicated hyperbolic function.
-$\sinh x = - \frac { 12 } { 5 } , \operatorname { csch } x =$
A) $\frac { 169 } { 25 }$
B) $\frac { 5 } { 12 }$
C) $\frac { 13 } { 5 }$
D) $- \frac { 5 } { 12 }$

Question

Quizplus · Accepted Answer

The hyperbolic cosecant, $\operatorname{csch} x$, is the reciprocal of $\sinh x$. Therefore, $\operatorname{csch} x = \frac{1}{\sinh x} = -\frac{5}{12}$.

A Value Of sinh⁡x\sinh xsinhx Or cosh⁡x\cosh xcoshx Is Given Use the Definitions and the Identity

A Value Of $\sinh x$ Or $\cosh x$ Is Given Use the Definitions and the Identity