8. (i) Sketch on the same diagram the graphs of $$y = \sin ^ { - 1 } x , - 1 \leq x \leq 1$$ and $$y = \cos ^ { - 1 } ( 2 x ) , \quad - \frac { 1 } { 2 } \leq x \leq \frac { 1 } { 2 }$$ Given that the graphs intersect at the point with coordinates \(( a , b )\),
(ii) show that \(\tan b = \frac { 1 } { 2 }\),
(iii) find the value of \(a\) in the form \(k \sqrt { 5 }\).