Question

If cosh x= 5/3 with x<0, find the values of the other five hyperbolic functions.

Answer 1

like with sine and cosine but instead use
\[ \cosh^2(x) - \sinh^2(x) = 1\]so
\[\sinh^2(x)=\cosh^2(x)-1\]
\[\sinh(x)=\pm\sqrt{\cosh^2(x)-1}\] substitute and get
\[\sinh(x)=-\frac{4}{3}\] (negative because x is)