Hi, at a point Q, x = (4+sqrt(17)
find the y co-ordinate, expressing your answer in surd form
x can also be written arsinh(4)
but I don't know if that helps.
I'm stumped :\
Thanks
Hi
$\displaystyle \cosh(\ln(4+\sqrt{17})) = \frac{e^{\ln(4+\sqrt{17})}+e^{-\ln(4+\sqrt{17})}}{2}$
$\displaystyle \cosh(\ln(4+\sqrt{17})) = \frac{4+\sqrt{17}+\frac{1}{4+\sqrt{17}}}{2}$
$\displaystyle \cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}$
$\displaystyle \cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}\:\frac{\sqrt{17}-4}{\sqrt{17}-4}$
$\displaystyle \cosh(\ln(4+\sqrt{17})) = (17+4\sqrt{17})(\sqrt{17}-4) = \sqrt{17}$