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.
-$\sinh x = - \frac { 4 } { 3 } , \tanh x =$
A) $\frac { 5 } { 3 }$
B) $\frac { 4 } { 5 }$
C) $- \frac { 4 } { 5 }$
D) $- \frac { 5 } { 4 }$

Question

Quizplus · Accepted Answer

To find $\tanh x$, we use the given $\sinh x = -\frac{4}{3}$ and the identity $\cosh^2 x - \sinh^2 x = 1$ to find $\cosh x$. Solving for $\cosh x$, we get $\cosh x = \sqrt{\sinh^2 x + 1} = \sqrt{\left(-\frac{4}{3}\right)^2 + 1} = \sqrt{\frac{16}{9} + \frac{9}{9}} = \sqrt{\frac{25}{9}} = \frac{5}{3}$. Therefore, $\tanh x = \frac{\sinh x}{\cosh x} = \frac{-\frac{4}{3}}{\frac{5}{3}} = -\frac{4}{5}$.

A Value of Sinh X or Cosh X Is Given sinh⁡x=−43,tanh⁡x=\sinh x = - \frac { 4 } { 3 } , \tanh x =sinhx=−34​,tanhx=

A Value of Sinh X or Cosh X Is Given $\sinh x = - \frac { 4 } { 3 } , \tanh x =$