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.
-$\cosh x = \frac { 5 } { 3 } , x 0 , \sinh x =$
A) $\frac { 16 } { 9 }$
B) $- \frac { 4 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 5 }$

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.
-$\cosh x = \frac { 5 } { 3 } , x > 0 , \sinh x =$
A) $\frac { 16 } { 9 }$
B) $- \frac { 4 } { 3 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 3 } { 5 }$

Quizplus · Accepted Answer

Given $\cosh x = \frac{5}{3}$, using the identity $\cosh^2 x - \sinh^2 x = 1$, we can solve for $\sinh x$. Substituting $\cosh x = \frac{5}{3}$ into the identity gives $\left(\frac{5}{3}\right)^2 - \sinh^2 x = 1$. Solving this equation for $\sinh x$ yields $\sinh x = \frac{4}{3}$, which is positive since $x > 0$.

A Value of Sinh X or Cosh X Is Given cosh⁡x=53,x>0,sinh⁡x=\cosh x = \frac { 5 } { 3 } , x > 0 , \sinh x =coshx=35​,x>0,sinhx=

A Value of Sinh X or Cosh X Is Given $\cosh x = \frac { 5 } { 3 } , x > 0 , \sinh x =$