5 A curve has equation \(y = \cosh x\) Show that the arc length of the curve from \(x = a\) to \(x = b\), where \(0 < a < b\), is equal to
\(\sinh b - \sinh a\)
\(6 \quad\) A circle \(C\) in the complex plane has equation \(| z - 2 - 5 \mathrm { i } | = a\) The point \(z _ { 1 }\) on \(C\) has the least argument of any point on \(C\), and \(\arg \left( z _ { 1 } \right) = \frac { \pi } { 4 }\) Prove that \(a = \frac { 3 \sqrt { } 2 } { 2 }\)