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.
-$\cosh x = \frac { 13 } { 5 } , x

Question

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.
-$\cosh x = \frac { 13 } { 5 } , x < 0 , \operatorname { coth } x =$
A) $- \frac { 12 } { 5 }$
B) $\frac { 12 } { 13 }$
C) $- \frac { 5 } { 13 }$
D) $- \frac { 13 } { 12 }$

Quizplus · Accepted Answer

Using the identity $\cosh^2 x - \sinh^2 x = 1$, we find $\sinh x = -\frac{12}{5}$. Then, $\coth x = \frac{\cosh x}{\sinh x} = -\frac{13}{12}$.

A Value of Sinh X or Cosh X Is Given cosh⁡x=135,x<0,coth⁡x=\cosh x = \frac { 13 } { 5 } , x < 0 , \operatorname { coth } x =coshx=513​,x<0,cothx=

A Value of Sinh X or Cosh X Is Given $\cosh x = \frac { 13 } { 5 } , x < 0 , \operatorname { coth } x =$