Question

Mk, I'm really not sure about this one. If it helps here is the multiple choice:
If sinhx=8/15, find the values of the other hyperbolic functions at x.

Answer 1

Use the relation:\[\cosh^2(x)-\sinh^2(x)=1\]

Answer 2

there are other relations you can use as well, e.g.:\[\tanh^2(x)=1-sech^2(x)\]\[\coth^2(x)=1+csch^2(x)\]

Answer 3

Well from elimination, it can only be 2 or 4 since sinhx=8/15, So cosh^2x = 8/15 + 1, correct?

Answer 4

correct?

Answer 5

not quite:\[\cosh^2(x)=1+\sinh^2(x)=1+\frac{64}{225}=\frac{289}{225}\]therefore:\[\cosh(x)=\sqrt{\frac{289}{225}}=\frac{17}{15}\]